Copied and pasted from a thread on the LTM forum a couple of months ago:
I was recently given this IIIc by my dad, who inherited it around 40 years ago. From what I can work out online, the Fl No. suggests it was made for the Luftwaffe - does anyone have a book to hand in which they can check the serial number? The serial number on the camera is 365884, and the number on the 5cm Elmar lens is 502052. From what I can gather online, those numbers give dates of 1940 and 1939 for the body and lens respectively.
It does look as though the rear of the top plate has been abraded, although I'm not sure it's enough to have removed an engraving. I think the screw in the top of the shutter speed dial must be a previous repair, and the threaded shutter button seems to be done kind of accessory - it unscrews with the shutter guard leading what looks like the original button below.
Does this appear to be a genuine Luftwaffe Leica? Either way, I've really been enjoying getting the hang of using it over the last 6 months or so! As well as the 5cm Elmar mentioned, it came with a 1937 9cm Elmar and a 1938 5cm CZJ Sonnar, which looks to have been converted to LTM using an Elmar focusing mount.