If the car shuts down fine with the booster disconnected and the hose plugged, but doesn't when the booster is connected - that's a pretty good clue that your booster has a vacuum leak - though there may be a valve in the vacuum line that could be bad, i'm not sure.

I seem to remember there being a rubber o-ring (or possibly a special seal) that went between the master cylinder and brake booster on my 300D. You may be able to back out the two nuts that hold the MC to the booster to see if that seal is there.

When I replaced my master cylinder, I found quite a bit of nasty old brake fluid inside the booster. One would hope that your mechanic would have pointed that out, but it's something to check (A good clue would be stripped paint under the cylinder on the booster)

It's not a very bad job to change out the booster, though I think I wound up disconnecting the cylinder to do so on my 123 chassis. (Something like four nuts that need to be accessed from under the dash, plus disconnecting the brake pedal linkage - and possibly replacing a bushing)