The wood is some type of European Walnut. The rifle was most likely made for some ranking Nazi official or someone in a high regulatory position since the war effort was consuming all production. The finish is at a custom level. The wood is completely filled - much nicer than later postwar production. Checkering patterns are also more much finer and more complex. The forearm checkering is wrap-around with a diamond pattern. I will attach a photo of it next to two later guns. You can see how much coarser the checkering is on the one on the far left in the photo is than this rifle.

John