I am collecting B.D.III markings myself and have done so for quite a number of years. This cap mark is not the typical rectangular stamp with manufacturer code and date that you normally see on B.D.III marked items.
Forgive me if I am screwing up my proper names on this.
rudolph, thanks for showing, it looks to be a nice "salty" model 1917 "Einheits-mutze", the cockades look to be correct for that late type cap being Officer style with cardboard black bases......the name of the material used in the construction of the cap was "Abzeichentuch" it matched the collar colour on the M1915 Bluse/tunic.
Prost ! Steve.
"The German Army is the perfectly adapted, perfectly running Machine. The difference is that the Germans are organised with a view to War...with the cold, hard, practical and business-like purpose of winning victories."
G.W. Steevens - The Daily Mail (1897)
I think on closer inspection you will find that this is a Jäger cap. The green is somewhat faded in areas, but in others you can see the grass green color. Another hint is the hand marking inside indicating either the 1st battalion of a Jäger Rgt. (1./Jäg.) or the 1st Komp. of a Jäger battalion.
It also appears that the cap is gray/green and not field gray.
I was thinking of going for this one but it looks a little too clean on the outside, do you think it's original?
Better shot of the stamps would help. Are there any marks from the cockades?