I pulled out Weimar Lugers and it has S.II as Schneidemuhl II (2nd) administrative district and is that an "n" after the II? That I am not sure about, if it was an "r" it would mean something, while an "n" does not?
If the S stands for Schneidemuhl, then it is a Prussian State Police grip strap marking.
But it makes for an interesting gun!
Ed