First thing I would do is never return to that local garage. The "prop shaft" doesn't move when in part. not likely to make noise if it is not moving. It sounds to me like you have a heat shield that has come loose and is vibrating.
If it's stationary when it's vibrating then it's unlikely to be the prop. Could be a gearbox fault or a worn or broken engine or gearbox mount, among other things.
Why not get a second opinion?
Its a deisel engined car and is normal
Hi, i got a 2007 auto Mercedes E280cdi sport, when i start my car in the morning it has a vibration noise in P and R, the vibrations seems to be coming from under the gearbox, i had it check by local garage and they say its the prop shaft, but the noise goes away when the car is warm and what if the gearbox just needs a service? The milage on the car is 132000