Not sure if you’re talking about guidance on physically moving it or something else like reserving the server’s IP address in the network, but you should be fine to simply pick it up and move it.

If the repurposed desktop is now massive or in a rack for some reason, you can always move one machine/box at a time. Unless the machine will experience a ton of shaking or dropping, there’s generally no need to take any hardware out if you’re just moving it to another room in the same building.