Original female Reichspost hat. There are a few small moth holes and one of the air vents is partly pulled through the cloth, but I would say the overall condition is still quite good. It should have an eagle, but that is missing, they generally come up for around $50 +/- so you should be able to complete this fairly easily. It has a sort of oilcloth lining. The only marking is a VI in pencil inside.
This bears a very strong resemblance to the first pattern visor cap and the lining makes me think it was probably made by Robert Lubstein. I thought it might be a visor hat without the brim, but there is enough difference to the visor cap that I do not believe this is the case. I believe it is probably a sort of "first pattern" female beret so to say. If it was a visor, it would have the celluloid film with the marker on the crown, but this hat doesn't have that and never did; it is made like a beret from the ground up. There is some hand stitching around the bottom edge, which was likely a period repair, I am assuming the leather sweatband was removed.
