diff --git a/autotests/export/lyx2lyx/lyx_2_2_test.lyx b/autotests/export/lyx2lyx/lyx_2_2_test.lyx
index 4e8e0d537c..9a652f1b8a 100644
--- a/autotests/export/lyx2lyx/lyx_2_2_test.lyx
+++ b/autotests/export/lyx2lyx/lyx_2_2_test.lyx
@@ -25,7 +25,7 @@ logicalmkup
 \font_sf_scale 100 100
 \font_tt_scale 100 100
 \use_microtype false
-\use_dash_ligatures true
+\use_dash_ligatures false
 \graphics default
 \default_output_format default
 \output_sync 0
@@ -94,11 +94,15 @@ Test reversion/conversion between 2.2 and 2.1 formats with lyx2lyx
 \end_layout
 
 \begin_layout Description
+BoxFeatures,
+\begin_inset space ~
+\end_inset
+
 colorbox: The word
 \begin_inset Newline newline
 \end_inset
 
-shadowsize at start of a line did trigger insertion of box options.
+shadowsize at start of a line must not trigger insertion of box options.
  
 \end_layout
 
@@ -123,7 +127,7 @@ backgroundcolor "orange"
 status open
 
 \begin_layout Plain Layout
-simple green frame around orange box
+framecolor "green" around orange box
 \end_layout
 
 \end_inset
@@ -173,24 +177,41 @@ thickness "0.4pt"
 separation "3pt"
 shadowsize "4pt"
 framecolor "black"
-backgroundcolor "none"
+backgroundcolor "cyan"
 status open
 
 \begin_layout Plain Layout
-no frame around cyan box
+framecolor "black" around cyan box
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+nested inset
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
 
  
+\end_layout
+
+\begin_layout Standard
+Fancy boxes have the colour chooser greyed out:
+\end_layout
+
+\begin_layout Standard
 \begin_inset Box ovalbox
-position "t"
+position "b"
 hor_pos "c"
 has_inner_box 1
 inner_pos "t"
 use_parbox 0
 use_makebox 0
-width "40col%"
+width "20col%"
 special "none"
 height "1in"
 height_special "totalheight"
@@ -202,16 +223,12 @@ backgroundcolor "none"
 status open
 
 \begin_layout Plain Layout
-no frame around cyan box
+framecolor at bol must not trigger replacement
 \end_layout
 
 \end_inset
 
  
-\begin_inset Newline newline
-\end_inset
-
-
 \begin_inset Box Shadowbox
 position "t"
 hor_pos "c"
@@ -219,7 +236,7 @@ has_inner_box 1
 inner_pos "t"
 use_parbox 0
 use_makebox 0
-width "40col%"
+width "30col%"
 special "none"
 height "1in"
 height_special "totalheight"
@@ -231,7 +248,7 @@ backgroundcolor "none"
 status open
 
 \begin_layout Plain Layout
-no frame around cyan box
+shadowsize at bol must not trigger insertion of box options
 \end_layout
 
 \end_inset
@@ -244,7 +261,7 @@ has_inner_box 1
 inner_pos "t"
 use_parbox 0
 use_makebox 0
-width "40col%"
+width "12col%"
 special "none"
 height "1in"
 height_special "totalheight"
@@ -256,36 +273,7 @@ backgroundcolor "none"
 status open
 
 \begin_layout Plain Layout
-no frame around cyan box
-\end_layout
-
-\end_inset
-
- 
-\begin_inset Newline newline
-\end_inset
-
-
-\begin_inset Box Shaded
-position "t"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 0
-use_makebox 0
-width "40col%"
-special "none"
-height "1in"
-height_special "totalheight"
-thickness "0.4pt"
-separation "3pt"
-shadowsize "4pt"
-framecolor "black"
-backgroundcolor "none"
-status open
-
-\begin_layout Plain Layout
-no frame around cyan box
+oval, thick
 \end_layout
 
 \end_inset
@@ -298,7 +286,36 @@ has_inner_box 1
 inner_pos "t"
 use_parbox 0
 use_makebox 0
-width "40col%"
+width "30col%"
+special "none"
+height "1in"
+height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
+status open
+
+\begin_layout LyX-Code
+double frame
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The background of 
+\begin_inset Box Shaded
+position "t"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 0
+use_makebox 0
+width "30col%"
 special "none"
 height "1in"
 height_special "totalheight"
@@ -310,20 +327,16 @@ backgroundcolor "none"
 status open
 
 \begin_layout Plain Layout
-no frame around cyan box
+shaded boxes
 \end_layout
 
 \end_inset
 
- 
+ is set in Document>Settings>Colors 
 \end_layout
 
 \begin_layout Standard
-The conversion must not change LyX code examples, e.
-\begin_inset space \thinspace{}
-\end_inset
-
-g., for fancy frames:
+The problem was detected in a LyX-Code example for fancy frames:
 \end_layout
 
 \begin_layout LyX-Code
@@ -352,8 +365,15 @@ shadowsize}{1pt}]{shadow}
 
 \end_deeper
 \begin_layout Description
-Hyphens vs.
- dashes in different context
+Hyphens
+\begin_inset space ~
+\end_inset
+
+vs.
+\begin_inset space ~
+\end_inset
+
+dashes in different context
 \end_layout
 
 \begin_deeper
@@ -440,6 +460,7 @@ LyX-Code
 hyphens -- ---; en–dash, em—dash;
 \end_layout
 
+\end_deeper
 \end_deeper
 \begin_layout Subsubsection
 ligature breaks inserted by lyx2lyx 
@@ -458,11 +479,7 @@ Rows of hyphens on subsequent lines -- ---; en–dash, em—dash and more hyphen
 \end_layout
 
 \begin_layout Standard
-
-\bar under
-H
-\bar default
-yphens with explicit ligature breaks -\SpecialChar ligaturebreak
+Hyphens with explicit ligature breaks -\SpecialChar ligaturebreak
 - -\SpecialChar ligaturebreak
 -\SpecialChar ligaturebreak
 -; en–dash, em—dash.
@@ -516,7 +533,7 @@ literal "false"
 \end_inset
 
  
-\begin_inset Formula $\ @{-->>}[r]$
+\begin_inset Formula $math--formula>>$
 \end_inset
 
  
@@ -550,6 +567,5 @@ set_width "auto"
 
 \end_layout
 
-\end_deeper
 \end_body
 \end_document
diff --git a/autotests/export/lyx2lyx/lyx_2_3_test.lyx b/autotests/export/lyx2lyx/lyx_2_3_test.lyx
index dbed95330e..46d28cfbb9 100644
--- a/autotests/export/lyx2lyx/lyx_2_3_test.lyx
+++ b/autotests/export/lyx2lyx/lyx_2_3_test.lyx
@@ -14,9 +14,9 @@ logicalmkup
 \language_package default
 \inputencoding auto
 \fontencoding global
-\font_roman "lmodern" "default"
-\font_sans "default" "default"
-\font_typewriter "default" "default"
+\font_roman "NotoSerif-TLF" "default"
+\font_sans "NotoSans-TLF" "default"
+\font_typewriter "NotoMono-TLF" "default"
 \font_math "auto" "auto"
 \font_default_family default
 \use_non_tex_fonts false
@@ -73,8 +73,9 @@ logicalmkup
 \tocdepth 2
 \paragraph_separation skip
 \defskip medskip
-\is_math_indent 0
-\math_numbering_side default
+\is_math_indent 1
+\math_indentation 3em
+\math_numbering_side right
 \quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
@@ -93,84 +94,12 @@ logicalmkup
 Test reversion/conversion between 2.3 and 2.2 formats with lyx2lyx.
 \end_layout
 
-\begin_layout Description
-allowbreak: 
-\bar under
-
-\begin_inset Box Boxed
-position "t"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 0
-use_makebox 0
-width "11em"
-special "none"
-height "1in"
-height_special "totalheight"
-thickness "0.4pt"
-separation "3pt"
-shadowsize "4pt"
-framecolor "black"
-backgroundcolor "none"
-status open
-
-\begin_layout Plain Layout
-
-\emph on
-simple
-\end_layout
-
-\begin_layout Plain Layout
-The em-dash is used—mainly in American english—without spaces.
-\end_layout
-
-\end_inset
-
-
-\bar default
- 
-\bar under
-
-\begin_inset Box Boxed
-position "t"
-hor_pos "c"
-has_inner_box 1
-inner_pos "t"
-use_parbox 0
-use_makebox 0
-width "11em"
-special "none"
-height "1in"
-height_special "totalheight"
-thickness "0.4pt"
-separation "3pt"
-shadowsize "4pt"
-framecolor "black"
-backgroundcolor "none"
-status open
-
-\begin_layout Plain Layout
-
-\emph on
-with optional line break
-\emph default
-:
-\end_layout
-
-\begin_layout Plain Layout
-The em-dash is used—\SpecialChar allowbreak
-mainly in American english—\SpecialChar allowbreak
-without spaces.
-\end_layout
-
-\end_inset
-
-
+\begin_layout Standard
+Part 1: Fonts: NoTo
 \end_layout
 
 \begin_layout Description
-baselineskip%: 
+baselineskip%: Box and rule with dimensions set to baselineskip% 
 \begin_inset Box Boxed
 position "t"
 hor_pos "c"
@@ -233,5 +162,136 @@ horizontal space insets using baselineskip.
 \end_layout
 
 \end_deeper
+\begin_layout Description
+rotated
+\begin_inset space ~
+\end_inset
+
+floats: (sideways environment)
+\end_layout
+
+\begin_deeper
+\begin_layout Standard
+sideways true at the beginning of a line must not confuse conversion
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement !ph
+wide false
+sideways true
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+[figure 1 stub]
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+rotated float 1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_deeper
+\begin_layout Description
+rotated
+\begin_inset space ~
+\end_inset
+
+float insets can be defined in a list: 
+\begin_inset Float figure
+placement !ph
+wide false
+sideways true
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+[figure 2 stub]
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+rotated float 2
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+new
+\begin_inset space ~
+\end_inset
+
+Babel
+\begin_inset space ~
+\end_inset
+
+languages: text parts in 
+\lang bosnian
+Bosnian
+\lang english
+, 
+\lang friulan
+Friulian
+\lang english
+, 
+\lang macedonian
+Macedonian
+\lang english
+, 
+\lang piedmontese
+Piedmontese
+\lang english
+, 
+\lang romansh
+Romansh
+\lang english
+.
+\end_layout
+
+\begin_layout Description
+Indent
+\begin_inset space ~
+\end_inset
+
+Formulas/formula
+\begin_inset space ~
+\end_inset
+
+numbering: 3em/right
+\begin_inset Formula 
+\begin{equation}
+y=x^{2}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
 \end_body
 \end_document
diff --git a/autotests/export/lyx2lyx/lyx_2_3_test2.lyx b/autotests/export/lyx2lyx/lyx_2_3_test2.lyx
new file mode 100644
index 0000000000..1d19f2fb33
--- /dev/null
+++ b/autotests/export/lyx2lyx/lyx_2_3_test2.lyx
@@ -0,0 +1,299 @@
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass scrartcl
+\use_default_options false
+\begin_modules
+logicalmkup
+\end_modules
+\maintain_unincluded_children false
+\language bosnian
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "cochineal" "DejaVu Serif"
+\font_sans "lmss" "default"
+\font_typewriter "lmtt" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf true
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype true
+\use_dash_ligatures false
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize 12
+\spacing single
+\use_hyperref true
+\pdf_bookmarks false
+\pdf_bookmarksnumbered true
+\pdf_bookmarksopen false
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks false
+\pdf_pdfborder false
+\pdf_colorlinks true
+\pdf_backref false
+\pdf_pdfusetitle false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 0
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 0
+\use_minted 0
+\branch branch1
+\selected 0
+\filename_suffix 0
+\color #faf0e6
+\end_branch
+\branch branch2
+\selected 1
+\filename_suffix 0
+\color #faf0e6
+\end_branch
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 2
+\paragraph_separation skip
+\defskip medskip
+\is_math_indent 0
+\math_numbering_side left
+\quotes_style polish
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 2
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Subsection*
+Test reversion/conversion between 2.3 and 2.2 formats with lyx2lyx.
+\end_layout
+
+\begin_layout Standard
+Part 2: 
+\end_layout
+
+\begin_layout Itemize
+Fonts: Crimson
+\end_layout
+
+\begin_layout Itemize
+microtype true
+\end_layout
+
+\begin_layout Description
+language
+\begin_inset space ~
+\end_inset
+
+bosnian: 
+\begin_inset Float table
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+table caption with bosnian prefix
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+allowbreak: 
+\bar under
+
+\begin_inset Box Boxed
+position "t"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 0
+use_makebox 0
+width "11em"
+special "none"
+height "1in"
+height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
+status open
+
+\begin_layout Plain Layout
+
+\emph on
+literal dashes
+\end_layout
+
+\begin_layout Plain Layout
+
+\lang english
+The em-dash is used—mainly in American english—without spaces.
+\end_layout
+
+\end_inset
+
+
+\bar default
+ 
+\bar under
+
+\begin_inset Box Boxed
+position "t"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 0
+use_makebox 0
+width "11em"
+special "none"
+height "1in"
+height_special "totalheight"
+thickness "0.4pt"
+separation "3pt"
+shadowsize "4pt"
+framecolor "black"
+backgroundcolor "none"
+status open
+
+\begin_layout Plain Layout
++ 
+\emph on
+optional line break
+\emph default
+:
+\end_layout
+
+\begin_layout Plain Layout
+
+\lang english
+The em-dash is used—\SpecialChar allowbreak
+mainly in American english—\SpecialChar allowbreak
+without spaces.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Description
+inverted
+\begin_inset space ~
+\end_inset
+
+branches: branch1 is off, branch 2 is active 
+\begin_inset Branch branch1
+inverted 0
+status open
+
+\begin_layout Standard
+normal branch1
+\end_layout
+
+\end_inset
+
+ 
+\begin_inset Branch branch1
+inverted 1
+status open
+
+\begin_layout Standard
+inverted branch1
+\end_layout
+
+\end_inset
+
+ 
+\begin_inset Branch branch2
+inverted 0
+status open
+
+\begin_layout Standard
+normal branch2
+\end_layout
+
+\end_inset
+
+ 
+\begin_inset Branch branch2
+inverted 1
+status open
+
+\begin_layout Standard
+inverted branch2
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+Indent
+\begin_inset space ~
+\end_inset
+
+Formulas/formula
+\begin_inset space ~
+\end_inset
+
+numbering: false/left
+\begin_inset Formula 
+\begin{equation}
+y=x^{2}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/development/autotests/invertedTests b/development/autotests/invertedTests
index 3105523792..6d925d104c 100644
--- a/development/autotests/invertedTests
+++ b/development/autotests/invertedTests
@@ -94,7 +94,6 @@ export/export/latex/unicodesymbols/.*_jis-platex_pdf2
 export/export/latex/unicodesymbols/.*_shift-jis-platex_pdf2
 export/export/latex/unicodesymbols/.*_utf8-platex_pdf2
 
-
 # Arabic
 # If we want to try to get it to work with pdfTeX:
 # - set all non-Arab text parts to a different language (e.g. English)
@@ -120,6 +119,9 @@ export/templates/RJournal_(dvi3|pdf[45])_systemF
 export/templates/aa_(dvi3|pdf[45])_.*
 export/templates/kluwer_.*_systemF
 
+# lyx2lyx tests:
+# back-conversion fails for rotated float inset in a list
+export/export/lyx2lyx/lyx_2_3_test_lyx.*
 
 # ================================================
 Sublabel: lyxbugs