The 1939 manufacture date is correct. But the pistol was probably a wartime "capture", either by the soldier named on the letter or by some other soldier who passed the gun on. In spite of "war stories", such captures were not always in combat, though pistols were more likely to be kept by the American soldier than rifles, most of which came out of depots or piles of captured arms when the solider was due to "rotate" to the States. Guns were also taken from German homes, from police, from collectors, and so on. Hundreds of thousands of civilian guns were seized and/or destroyed; the Second Amendment did not apply to citizens of the Third Reich.
That letter was not needed until an American soldier wanted to bring the gun back to the States, at which time he applied for a letter to get the gun past US customs which was the reason for it. (No, GI's didn't call "time out" in combat and take captured materiel to the CO to get a letter; many guns lettered to a given soldier had been passed around for months before someone wanted to bring the gun back and got a letter.)
I need not point out that when the GI proudly displayed his "capture gun" to his friends, he usually added modestly that he had personally taken it from at least a field marshal, if not Hitler or Goring.
Jim