I'm inclined to say after, but it may work with Laplink as well.

Microsoft may be more concerned now about active licenses not installed licenses. If you use it on one machine at a time, you may be ok to install on the old system and Laplink it over if only one machine is running Office at once. (With a 1 seat license.)

It seemed to me late last year Microsoft started verifying licensing every time you started any of the Office apps when none were running. This is inconvenient if you are not on the Internet always. It probably allows Microsoft to keep a tighter leash on licenses but may allow switching between machines easier.

If you will be disconnected from the Internet, such as onboard aircraft, start one office app before you disconnect from the Internet and leave it open. This holds a license locally and lets other Office apps to start.