Final Cut bought with a different Apple ID

Years ago I bought Final Cut for my iMac and last year I had to change my Apple ID. I can still use Final Cut and I can update it using the old Apple ID, which only is a short term solution, though.

Is there a way to associate my purchase of Final Cut to my *new* Apple ID?

(Before someone asks the obvious question: when you change your Country of residence you are pretty much forced by Apple to change your apple ID unless you maintain your email and bank account in the Country you left, which oftentimes is not possible.)

Thanks!