That's amazing since the laptop and the desktop have such different hardware. You'd expect some or even a lot of things not to work.

If it's already validated it's quite well possible that there is no need to validate it again. But don't complain if it asks for
validation and it will be refused. After all, the license is void, because it was only valid for the original laptop. So I'd keep the original hard disk of the desktop as a fall-back option.

Kees