First Luger! BYF 41

My most recent pick up, 1941 dated Mauser produced P08 Luger. I was told by the seller that it’s an S/42, but I don’t believe that’s the case. All numbers matching, been professionally refinished. Must of made its way to Great Britain at some point, as it has British proofs under the barrel, and from what I’m told, initially came to the person I received it from coated in the hardened black paint finish on many postwar refurbished Enfields. Came with two magazines. Seller told me one was the “correct” one and the other was for a Luger, but not this Luger. Which ones which? I noticed they have subtle differences in finish and shaping on the thump pad used for loading. One is serialized and the other is not. Can anybody tell me anything else about the pistol? I’m not very well versed in these.

It's a byf'41. The first one pictured with the blank bottom is a post war, aftermarket magazine. The second one is an appropriate, wartime magazine made by Mauser with the same letter block as the pistol.