For his height the frame might be right, frame size isn't all about absolute height after all, if he is going to sit on it like a shopper (no offence intended) then it is hard to really comment, he needs to assume an appropriate position on the bike, this may take some getting used to it.
This image attached it only for example purposes, but guessing at the location of his ankle, hip, shoulder and elbow joints, the white line is his current position, the green line is where a forward rotation of the hip and a slight bend in the elbow would get him.
This might not be comfortable, it is just an example of how a small change in posture would quite dramatically alter his position.
A racey position would have the ankle to hip line at 90 degrees to the hip to shoulder line and the shoulder to elbow line at 90 degrees to the hip to shoulder line. For the OP, a full on race position would require a longer stem almost certainly.