The lens has a serial number on the front in the black paint ring. It is in plain sight there. Just too un-detailed to read. It is often missed on these collapsible Elmars.
Also, I'm with Robert here on this possibly being genuine.
I find it pretty typical that on both his camera and yours, the letters that appear twice ( U, T and E in Luftwaffen - eigentum) are very slightly different. Those engravings were done by hand and a forger would probably have succeeded in getting them exactly similar, or not that similar at all.
The slight amount in which they differ, makes me think they were engraved by the same person.