The normal WWII military Luger serial number markings are the full serial number, including the suffix letter on the front of the grip frame and on the magazine, and the full number less the suffix on the left side of the receiver above the trigger guard. Other parts normally had only the "last two" numbers.
There is a lot of variation in Luger serial number placement over the years and over the several makers and contracts, so the exact placement will depend on several factors.
The barrel serial number is normally on the bottom, so I am not sure what is on the top on Mr. Daily's pistol. Perhaps he will provide some pictures to help determine what he has.