Cluster "float" is common. (Since the axle does not rotate, it is not the culprit.) Grab onto the cogset and check for excess play. One can reduce play in an old-fashioned freewheel by loosening the retaining ring (CLOCKWISE), removing one of the shims, and retighening the ring (anticlockwise). If your friend is very unlucky, the freewheel may be cross-threaded on the hub, which would cause pronounced freewheel wobble, even in the absence of bearing play.