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.