What files are in folder C:\Windows\SysWOW64\Macromed\Flash?
What means "does not work" - what do you see instead of the working Flash Player?
Can you try a clean install, then try again: http://forums.adobe.com/thread/928315
Download the 64-bit installers from http://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html#Ins tall_in_a_firewall_proxy_server_environment (they do indeed install both 32-bit and 64-bit Flash Player).
Thank you for your suggestion.
I did the clean install with the 64-bit installer as suggested by Pat. On IE9 64bit and Firefox, the Flash content is shown.
Unfortunatelly the IE 9 32bit does still not show me any Flash content. If I check with IE 32bit on the Adobe website, it does though tell me that "You have version 11,2,202,233 installed", but no Flash content displayed.
I can for example not reply to this thread in the IE 32bit either....