Unfortunately, I strongly believe that this cap is a fake. While it certainly seems to look old, there are too many errors in construction that can't be explained away. I can see that maybe the original untrimmed peak may have been replaced some time by this trimmed peak, however, I can see no reason why the sweatband would be replaced. Original sweatbands were machine sewn to both the lining on the top edge and the cap body on the bottom edge. In addition, the stamps make no sense. Where would not be an inspector stamp (SL) without the inspection depot stamp and date showing final approval.
The cap looks good on the surface, but I am convinced it is a fake.