Different urn:uuid for same Adobe ID on different devices

I recently moved to a new Computer, installed ADE and authorized with my Adobe ID (the very same account I am posting with right now).

I tried to import my e-books, but was presented an error message that told me that the books I tried to import are licensed with another account.

When I tried to open the books, ADE presented me the authorization dialog and after entering my login data again it told me that the Element i tried to open is not linked to the account I entered.

I compared the authorizations on both computers and noticed that, although they are both authorized with the same e-mail address, the urn:uuid is different.

I guess this is the reason I cannot open my books.

What is the problem here? What can I do to access my books?