I am not with Laminar Research; just a flight simmer from down under.
To move X-Plane from one PC to another is quite simple. It is just a matter of "cut and paste"
Follow the advice from disc provided your original installation has been loaded onto your desktop or into a dedicated directory on your "C" drive and not within the operating system files.
Copy and paste X-Plane onto a portable drive of sufficient capacity from your old PC. Then connect that drive onto your new PC and then copy and paste onto your new PC into a "dedicated" location. It needs to be a dedicated location as X-Plane will not work if you paste into other file directories.
Everything should work as disc has indicated.
Be advised however, if you want to run 2 copies of X-Plane at the same time on each computer you will need to purchase another legal copy of the software along with the product key. If you have a digital version you also have to be connected to the internet at all times as while you are running X-Plane I understand the software is also running a verification process to ascertain you are running a legal copy. I understand if running 2 versions at the same time on one legal copy at least one possible 2 will shut down.
Have a look at this link found at https://www.x-plane.com/kb/x-plane-digital-download-xdd/
Good luck with your new PC.