When receiving the serve in doubles, does the non-receiving partner have the right to move, or must he remain immobile until the first service motion?
The laws of badminton state that the partners of the server and receiver may take up any positions they like that do not unsight the server or the receiver. Nothing is said about the partners being stationary, so they can move all they want.
Probably not, unless the intention for moving about is to distract the opponent, for which there is a rule against.