The Panzerfaust 44 "Lanze" (Lance) was a light, shoulder-fired anti-tank rocket of the West German Bundeswehr in the 1960s and early 1970s. The "EX" marking means it was an exercise or dummy round for training.
This dummy projectile came to the Smithsonian as part of a transfer of German rocketry artifacts from the U.S. Army Ordnance Museum in Aberdeen, Maryland, in 1989.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.