$ sudo mkdir -p /opt/Obsidian
$ mv ~/Downloads/Obsidian-0.13.19.AppImage /opt/Obsidian
$ sudo vim /usr/share/applications/obsidian.desktop
[Desktop Entry]
Name=Obsidian
Exec=/opt/Obsidian/Obsidian-0.13.19.AppImage
Terminal=false
Type=Application
Icon=obsidian
$ copy /path/to/obsidian.png /opt/Obsidian
$ sudo ln -s /opt/Obsidian/obsidian.png /usr/share/pixmaps
You can extract the icon and the desktop entry files from the AppImage.
$ /path/to/Obsidian.AppImage --appimage-mount
/tmp/.mount_ObsidiXXXXXX
Just search the files in /tmp/.mount_ObsidiXXXXXX
.