S80 2003 transaxle and drive shaft problem

[Cumbac]

I have just taken possession of an S80 2002/2003 model and noticed a vibration while driving, like wheel balance. This happened at around 50 to 60 mph and under light acceleration. Coasting would be smooth. I got the wheels balanced and the rear control arm bushes replaced.. It was better but vibration still present. Took it bck to the tyre place and asked mechanic to make a good check of the cv joints, steering, etc. And he found that the left hand drive shaft inner cv body can move, ie the transaxle drive shaft coming out of the transaxle is loose and can move around by about 2mm. It should be firm of course. Has anyone had this problem? Could it be the drive shaft itself (worn) or the bearings inside the transaxle (differential) .
Does anyone have a diagram of this part of the transmission they could let me have to show to my mechanic. Is this going to be a major repair?? Thanks for any help