I have seen this kind of pain come and go a lot among lifters with no real diagnosis and no treatment. I think any hand and wrist mobility work will help, but also take a closer look at his snatch grip and his hand position in the snatch since that's the lift that causing him pain. If he's holding his hook grip overhead, make sure he's flexible enough to do this and that he's achieving a good hand/wrist position rather than, for example, trying to hold a neutral wrist and/or gripping the bar too tightly.
Also to consider:
Did he recently change his grip? Did he recently significantly increase his snatch training volume? Did he recently make a big PR and then increase his training weights significantly and suddenly?