Well, that thing is off the charts kewl as all hell. You should see the POS anemometers duh Gubmint buys today. That thing looks like a Swiss watch. Really, that could be used by anyone who needs a wind value, as it's so compact. However, IMO the threaded base sort of rules out Navy. It looks like you can screw it into wood so it stays put. The Parteiadler in the case indicates something special for a Nazi Unit (SS) rather than Wehrmacht. You see those on SS arms as well.
I've never heard of it either, but there it fucking is! That this was for an SS unit adds a ton of verisimilitude that it's for a sniper. Highly unlikely that an artillery or mortar unit would have such a device (but i suppose it's possible). The label could be something that a GI added when he snatched it. The piece itself looks legit to me.
So while I've never heard of that either, it's sort of hard to come up with an alternate explanation for the piece. You should contact him and ask him what makes him think that's the origin. He has another, larger, one that he is also claiming is from a sniper school. He may have providence. You don't know unless you ask.