ANSWER for all with the same issue:

First you need to contact Adobe Support and get permission to waive the early termination fee for stopping payment of Captivate early.  

Then you have to deactivate Captivate in your account. Captivate > Help menu > Account

Then you close Captivate and open it again (I had to do this twice and wait a short while) and it will ask for your serial number.

Then enter the free serial number they gave you and it will work. 

Double check by exiting Captivate and reopening again.

Then you should see an email that tells you that Captivate subscription was deactivated, and another from Adobe Support that says they waived the charges.  Check for these to prevent payment problems.

You cannot have a Captivate license which is subscription, combined with a perpetual license (serial number) with the same Adobe ID. Not even when they are in a different language.

If you have a running yearly subscription, they should rather have extended that for 3 months free of charge then send you a Serial No for another instance of Captivate. Unless you want to have Captivate TWICE for three months for whatever reason, turn to Adobe Service and ask them to revoke the license key you received and extend your subscription accordingly instead.