Unbelievable... after 4 weeks of trying... it was successful!
Many thanks @ all, especially @kglad and @user_34532 !
This link of user34532 leaded to success: www.adobe.com/go/getactivated ...
This link I found was helpful too: https://helpx.adobe.com/de/creative-suite/kb/serial-number-validation-launching-cs6.html
Step by step:
1) I installed CS6 on my MacPro (offline) from my DVD without inserting serial number.
2) After Installation I opened Photoshop.
3) When asked for the serial number I clicked “no connection to the internet“ on my MacPro
4) Than I clicked “Generate request code“ on my MacPro
5) I opened this link on my iMac (online): www.adobe.com/go/getactivated
6) I opened this link on my iMac: Generate a Response Code
7) I copied the request code from my MacPro and inserted it (via usb-stick) into the form on my iMac
😎 I inserted my serial number into the form on my iMac
9) I clicked “generate answer code“ on my iMac
10) I copied the answer code from my iMac and inserted it (via usb-stick) into the Photoshop window on my MacPro
11) I pressed “enter“ and saw the popup that made me happy: Offlineactivation completed. Creative Suite 6 has been activated successfully and can be used now.
