Model 37 snub nose serial number 16823. Can my father safely shoot +p through it?
Take the serial number from the location in the pic and include any letter prefixes such as "J". If that is where you got from then it would date to 1952 which is 5 years before S&W began stamping model numbers on the gun.
+P is not recommended for the aluminum frame guns. It won't blow it up but it will accelerate wear.
K148XXX on bottom of the grip
Serial numbers ran from K136691 to K175637.
It's a K-38 Combat Masterpiece which became the model 15 when S&W began assigning model numbers in 1957.