PDCs are supposed to be stationary, imbedded into the planet in a mountainside or something . However there seems to be a bug which occasionally causes stationary stuff to move?
You can use Spacemaster to move task groups however, turn spacemaster on, then load the task group window, select the group the PDCs are in, select the history/officers/misc tab , on the right side is a menu to select a system and body, use save to move the task group there.