Correct. Thompsons were standard issue SMGs in Italy as well. The STEN wasn't issued to 1Cdn Corps until after they re-located to NW Europe in early 1945. That P14 sniper rifle is a head scratcher though.
Lots of Winchester P14's were converted to sniper models at the end of WW1, and since No4(T)'s weren't in wide spread issue before 1944, more than likely this lads unit was issuing converted P14's to its snipers.