Issue
Recently in LAB it happened that I had to reuse a environment previously cloned.
When on the new NSX-T 3.1.2.1 I tried to add the vCenter (cloned) into the "Compute Manager" I have been warned with the following message:
Compute Manager <vCenter_IP> is already registered with other NSX Manager <NSX_Manager_IP>
Solution
To add the vCenter at the new NSX-T Manager is enough select the error message and click on RESOLVE ...
... Close the warning message ...
... re-insert the Username and Password of the vCenter and click RESOLVE...
... and the vCenter will become successfully registered.
That's it.