A couple years ago the local-to-me Cabelas had a French 12 ga double go through the used gun rack, bearing similar German and French proofs but neither the alleged Himmler signature, the LW eagle, nor the award language. It was a nice gun overall and in nice shape. The German proofs were the Suhl proofhouse (like this gun's) and also dated 741. Additionally, it had a few "SuS" monograms stamped into the buttstock and, IIRC, the watertable or the flats.
I had two suppositions about that gun at that time. My one supposition was that the Germans had looted a number of French doubles and, prior to turning them loose into commerce in Germany, had them run through Sauer's hands and the Suhl proofhouse just to be sure. These guns are light to begin with. Their barrels tend to be lightly struck to pull that off, so belt-and-suspenders Germans would want their own proofs to make them more salable. An alternate supposition at that time was it was a "double GI bringback" - first brought back to Germany by a German soldier, then reproofed in Suhl for some bureaucratic reason now lost to time, then back to the USA in some troop's duffel.
In either case, that was a nice gun in good shape and a good match to my French 16, but Cabelas wanted $750 for it and I thought that a good $250-300 too high, especially since it too had 65mm chambers. So I passed and someone else got it.
Seeing this gun tells me I should favor the first of my suppositions - that the Germans looted a bunch of guns and shipped them home to supply their home market, done in an organized manner. The 741 proof date (on both this one and the one I saw) tells me they went through in a bunch. I would be willing to bet that the records of the Suhl proofhouse, if they still exist for that time, would reveal something along those lines.
I disagree a bit with the translation - Scharfschuetze is not necessarily "sniper". It can also mean simply "best shot" or in this context "high overall shooter". In the case of this gun, it's a nice, though generic, double which quite easily could have been given as a prize to the best shooter in some competition or other. The Luftwaffe eagle and swastika on the one hand and Himmler's alleged signature on the other seem a slightly odd juxtaposition. I can speculate any number of reasons why it wound up that way but in the end it doesn't really matter. I would bet the farm on it never having passed through Himmler's hands.
Not wanting to offend anyone by the comparison, knowing how sensitive - rightly - a lot of people are to Himmler, his acts and what he stood for but to give an example, is the presidential signature on your Eagle Scout diploma really real? Mine isn't.
Speaking for myself, if this gun didn't have the Himmler signature engraved and the swastika, I'd view this as a nice example of base model French 16 made into a presentation piece and I'd welcome it in my cabinet. At about $400 or so.