ENM,
First off, the gun was marketed by Otto Bock, as you said and it is plainly so marked. I don't believe it is a JP Sauer, however. There is a marking on the rib, partially hidden by the edge of the photo, that seems to be BSW. This would be "Berliner Schuler Werks", which was one of the names Simmons used while they were desperately trying to avoid the NAZIs taking over their company. It was a Jewish family owned company during a time it was becoming more and more difficult to be Jewish in Germany. Also there was residual resentment by other manufacturers because Simmons was allowed to work after WW1 for the German Army. I believe the S on 3 triangles was their logo. It was proofed in Suhl, during July 1936( 736). The 12 in a circle, over 70 mm, means it is 12 ga, with 2 3/4 " chambers. Since the standard German chamber was shorter than this in 1936, the gun may have been made for export to the US( not positive). The crown U under the eagle is the mark for a View proof, after a definitive proof. This view proof amounts to a detailed inspection, including verification of dimensions. The 13/1 is the diameter of the bore, ahead of the chamber, expressed in gauge measurement. This equates to about 18.26mm. The crown W, means the barrel is choked, but the amount of constriction in not shown. The Nitro means it was nitro proofed( ie smokeless powder). There are several other marks that I can't make out. If crown S is included( and it should be), this means it was proofed to fire shot. It has fluid steel( Fluss Stahl) barrels. The steel company was "cut off" by the edge of the photo, but was often Krupp. It has cocking indicators , interrupting sears, and better than the basic engraving. I am not up on the "grades and models", so I won't be of much help in that regard. JP Sauers are very fine guns, but I believe this Simmons is much more interesting, due to the history. The Simmons family was recently able to regain ownership of the company. I hope you find this helpful.
Mike