I did not use Rhino on another computer.
The full history:
I used Rhino 6 locally, then moved it the the Cloud Zoo to see how the cloud zoo works. After that I moved the license back to local. Everything worked fine with Rhino 6, local and using the coul zoo.
I upgraded to Rhino 7, got an upgrade key. When installing Rhino 7, I got the folowing error:
I did not have the opportunity to enter the missing serial number
Then I put my Rhino 6 license back to the Cloud Zoo and updated the Rhino 6 license to a Rhino 7 license on cloud zoo. This worked, but I only had a Rhino 7 license after that in the Zoo and Rhino 6 is not able to use this license. Installation of Rhino 7 worked fine by logging into my Rhino Account.
I took the license back to my local computer. Rhino 7 works well with it. But Rhino 6 complains as explained in my first post (I am trying it with the old RH60 key).