I would recommend staying on the lighter side of the range of bullets. Any of these will kill a mule deer.
Further he should shoot that gun from a few different positions and be sure that the scope is adjusted to his vision. I have had a number of hunters over the years shooting larger guns that they are not familiar with "scope" themselves. Ending up with a bleeding eyebrow and much embarressment at camp. Usually not being able to make a followup shot.