That is the old Brunswick Process. It does work, as I've done this with a couple of other balls. Yes, 400 grit (that's US/CAMI grade, NOT FEPA grade, the grading for Abralon and Siaair pads.
It works even though 400 grit is rough, because Brunswick's High Gloss Factory Fniish polish is an extremely abrasive polish. Use a good amount of polish and firm pressure and burn it in. (Actually, be careful as you may not want to burn it in too much. It will go too long and snap too unpredictably.) At the end there should be a relatively high gloss finish and there will be very few sanding lines visible.
Sand it to 400 grit, de-oil it, then polish. He should be very surprised and he will have problems using it because it will act like nothing he remembers because he has used it in an abused state for so long. That will be the hard part for you, as he wonders how you destroyed his ball.
Good luck (with your good deed) !