The US formed no new units with P-40s after 1943. A-36 units in Italy may have gotten P-40s due to shortages of replacement A-36s for a short period of time in 1944. P-40s using Allison engines may have been seen as requiring minimum training for ground crew. Units were converting to P-47s within weeks or a couple of months. The P-40s may have already been in theater and/or been planes turned in by P-40 units converting to P-47s.
By 1944 the "new" P-40s were going mostly to allies as lend lease. The last few hundred built went directly to scrap yards.
I think by the summer of 1944 Italy had become a sort of back water. Italy had changed sides US forces took Rome on 4 July, and the German military was getting out ASAP. This all stems from a quote from wiki, but I could see sense in using P40s to replace lost A36s in Italy engines are the same and I believe many pilots had flown P40s prior to the A36.