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Cross draw P38...
The answer is yes. First off, many of WWII soldiers were sons of WWI soldiers. Many were also hunters or shooters before the war. They would have known, and used 9 x 19 mm weapons and ammunition. The STEN is a 9 mm weapon. Commonwealth forces in particular would have had ready access to 9 mm ammunition. US forces, might not have had the ammunition in their supply system, but as said above, captured ammunition (and weaponry) was readily accessible.