Stuka must be a nickname or a fantasy name multiplied on the net. I couldn't find any reference to it in my books. In January 1938 this prototype was ordered after in 1937 a VW 30 was stripped in order to test its offroad abilities. The prototype Typ 62 was finished in late 1938 / early 1939.
There is one car around claiming to be the surviving prototype, but at least the chassis number belongs to a 1951 VW:
This is interesting because I have previously seen pictures of this car on the internet clearly stating that it was a reproduction, built as such. I'm afraid that as with some other previous modern copies, someone is muddling with the truth trying to create a new history for this car.
Additionally, I'd like to slightly alter your chronology of the Typ 62 prototypes. The stripped VW 30 you mentioned was designed from 1936 and ready by the following year; this
Porsche Kriegsfahrzeug was the very first prototype of what would ultimately become the Kübelwagen. Then the car of the puzzle is indeed the
Porsche Geländewagen 62, but it was actually built a little early than you state, in February 1938, then tested by the military from the following month. The third and fourth prototypes were the
Porsche Typ 62, built in November 1938 with two different bodies (a more rounded body, and a square one close to the final Kübelwagen, both built by Trutz), so I guess the dates you mention come from these ones. The next step was the
Porsche Typ 62B, built as a pre-series to the Kübelwagen from October 1939 and tested by the Wehrmacht in actual operations from December. Then came the final Kübelwagen.