CMF is Central Mediterranean Force - the overall title for the Allied Forces in Italy after the invasion of 1943.
38 PTC was one of about a dozen PTCs in Italy whose role was the holding and processing of reinforcements, training, rest camps, and managing personnel in transit on leave, back to UK, off to other postings and the like. People usually spent only a short time in a PTC but the units required a staff to run them who would spend longer there. 38 PTC moved a lot, can you give the start/finish dates?
Is the unit you quote 2721 Field Squadron and was he with them throughout apart from the PTC?
MaxD