A pressure cooker has more small removable parts than most kitchen appliances, and every one of them matters for it to seal properly again. Pull them out, bag them together, and the main pot is easy from there.
Pro tip: Replace the sealing ring if it already looks worn before the move, since a compressed or stretched ring after packing is a good excuse to swap it anyway.
Watch out: Never pack a pressure cooker with the sealing ring still installed in the lid and something set on top, since crushing weight can permanently deform the silicone seal.