Now I tried again, actually the old package was used, more to that below.
The Memo content works now!
There is still an issue with the vertical scroll bar (see attached screenshot), the horizontal one seems to work.
This time I didn't attach a demo project, its enough to change the ScrollBars setting to ssVertical to see the problem. It occurs in both cases, when the PaintTo is called directly and when its called in the parent control.
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About the installation, its a bit strange. The package richmemopackage.lpk is needed, but can't be installed. The package richmemo_design.lpk in the subdirectory 'ide' requires the richmemopackage and recognizes it once it was opened in Lazarus. After uninstalling the old version of richmemo_design.lpk and reinstalling it, it still used the old version of richmemopackage.lpk. Then I deleted the richmemopackage.lpk, and tried to install richmemo_design.lpk -> richmemopackage.lpk missing. After just opening the correct richmemopackage.lpk in 'menue/package/open package file', the richmemo_design.lpk could be installed.