Lerk,
As a Lee has advised, once you have changed to your new Pi (which can now be a Pi3B or Pi3B+), send an email to
support@pilotaware.com with your name, email and the MAC addresses of both your old and new Pi. Ash will then change over your registration to your new Pi and e-mail you a Licence Key for your new unit which will run for the remainder of your existing licence period.
When the new licence is about to run out you will get an e-mail advising you how to renew via the website at
https://pilotaware.lode.co.uk (the same site from which you will have downloaded your software update).
Regards
Peter