I agree that the rifle is most likely a parts gun. Who or when it was assembled is anyone's guess. If all parts are LB, this would suggest some connection to the factory or military.
The wrist certainly shows no evidence of a number ever having been there.
Inglis pistols assembled from parts are not unheard of.
My only experience with military munitions production was working on a line making 2.75" folding fin rocket warheads during the Vietnam era. While there was a lunchbox inspection every time you left the plant, they were more concerned about the theft of tools or the auto electrical components also manufactured there. It certainly would have been possible to pitch a warhead or two over the fence during a break on a nightshift. I always thought that a pair would made a couple of interesting table lamps. Never did get around to acquiring a couple of our rejects.
There are two known specimens of the Mauser made copy of the Mk.II Sten. The one in the Oberndorf museum was stolen from the plant by a worker, and subsequently turned in.