I saw a classic black and white film in perhaps 2010 on TCM or AMC about a soldier who had taken the clothes and identity of another soldier who was dead. I think he also had facial injuries that made it so others could not tell who he was. I think there was a court scene and for some reason I recall that he “proves” he was the dead man using a watch found in the dead man’s coat pocket.
I don’t think there is a watch, but otherwise it sounds like The Imposter (1944).
http://www.tcm.com/tcmdb/title/497300/The-Impostor/