I swear I really tried hard and looked very hard for information. I never could transfer that pro license from one computer to another, an inifinite maze of unhelpful Microsoft web pages, wasted hours on this.
I was extra paranoid and make sure I copied the license key somewhere, etc. I can't remember if I had any small issues but I think it was pretty straight forward.
I recently had to turn on my old PC and even though it's unlicensed it still works is if it was "Pro" licensed.