Pretty sure it's a J.P. Sauer & Sohn. Not sure what model . Looks to be in great shape. Some of these are Nazi marked so look closely! Although this appears to have the magazine release on the grip; this is typical of later U.S. spec weapons. Still worth a little more research!
Appears to be a model 38H, or just H. Second pattern with thumb safety. However the grips would not have been yellow (or "ivory") in WWII German military use. Close-ups of the barrel (pointing left) and rear of gun (pointing right) will help us see the markings and figure out if things look correct.
The white plastic grips were probably put on the gun after it left German service at the end of the war. To my knowledge no German service guns had other than issue grips. Nice gun.
4th Wehrmachts-Variation (military-finish with E/37 acceptance mark without manual safety-lever; approx. 10,000 pieces) with the following characteristics: Characteristics:
[TABLE="width: 100%"]
[TR]
[TD="width: 135"]Legend:
[/TD]
[TD]Cal. 7,65
[/TD]
[/TR]
[TR]
[TD="width: 135"]Finish:[/TD]
[TD]military-finish blued[/TD]
[/TR]
[TR]
[TD="width: 135"]Grips:[/TD]
[TD]black Bakelit-grips with "SuS"-Logo on left side; checkered[/TD]
[/TR]
[TR]
[TD="width: 135"]Serial number:[/TD]
[TD]6-digit number left on frame 3-digit number inside slide 3-digit number rear of breech block
[/TD]
[/TR]
[TR]
[TD="width: 135"]Acceptance stamp:[/TD]
[TD]E/37 left on frame
[/TD]
[/TR]
[TR]
[TD="width: 135"]Test proof stamp:[/TD]
[TD]E/N right on frame E/N right on slide E/N on barrel (near muzzle)
I can see what appears to be a set of waffenampts (German proof marks) on the original photos. I'm not sure on the grips, but if they are replacements originals are out there if you wanted to replace them. That pistol is worth a few bucks too..... I've seen them go for anywhere $700 plus