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GG/P 40, H.E.A.T. Rifle Grenade
This is the first German Rifle Grenade of WWII developed by the Luftwaffe in 1940 (?) and saw use with paratroop units. 
It has a 60mm shape charge warhead. 

Gewehrgranäte zur Panzerbekämpfung ("rifle grenade for fighting tanks") 
Used in conjunction with the spigot launcher:
Schiessbecher mit Klappkorn ("discharge launcher with folding post")
There were two types: a blunt nose version (shown here) and a later type with a tapered "standoff" nose cone design. It was superseded  in 1942 by the more familiar cup launcher.

Many thanks to Wolfgang for taking the time to send me data on this grenade. 
Now I just need to translate the German text! -ej

The spigot launcher utilized a bayonet-like mounting design and had a flip sight, which was used in conjunction with a rear clamp-on Hilfsvisier "Auxiliary sight"
There were range graduations from 25 to 100 meters.

Here are the main components of the GG/P 40:
A sheet metal hollow charge warhead followed by the base-detonating fuze assembly "AZ2492" (dated 1941), a sheet metal tail boom and rubber base plug. 
I'm guessing a launching round was probably stored in the tail and the plug was a stopper to hold it in. 

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