Assuming the inscription is correct, 350th Infantry was organic to the 88th Infantry Division, which served in Italy. He died 30 September 1944 but wasn't necessarily a combat casualty ("PH" at the base of his marker indicates he was awarded the Purple Heart but no way to determine from the scant info at hand whether this was awarded posthmously - for wounds that resulted in his death - or for a previous incident).
His deceased file should indicate the date he was injured (if different from his date of death) and the locale of injury or death (or both). You'll find instructions on how to order the file at Message #2112.
The division veterans association may be able to put you in touch with someone who remembers him.
88th Infantry Division Association Post Office Box 925 Havertown, Pennsylvania 19083-0925 (215)533-9170
88th Infantry Division Association Post Office Box 6510 Albany, California 94706-0510 (510)526-0385