I can't know all and everything, but in my opinion that isn't German military equipment.
German military used leather helmets since round about 1870 and tent sheets as poncho, in the beginning rectangular, than they changed to steel helmets, in WW2 came the triangular tent sheet poncho, than in DDR back to larger rectangular and to the US type tent sheet in western Germany, used as a poncho with additional hood.
The US Poncho was in western Germany spare equipment for chemical attacks, Bundeswehr used the tent sheed as poncho until they got rubber suits and later Goretex suits.
I spend a lot of time in surplus shops since decades, but I never have seen this hood!