He's probably at the point where he is now fearful to have a bowel movement or refuses to. The problem here is that the longer the hold the poop in, the more the poop loses moisture and makes it even harder to pass.

Increase fiber at snack and lunch (blueberries, prunes, prune juice, flax seeds etc.).

Also, talk to the parent about Lansoyl. It tastes and looks like red jello but has something like 80% mineral oil. It makes it impossible for your child to hold in their poop. I've used it before with one of my children and it worked amazingly. She refused to go poo because something had the time had scared her about it, and she held it in and made herself constipated. I tried the prune juice but the lansoyl worked quickly for me to alleviate the problem. Once she had her BM I just made sure to increase her fiber intake and reduce binding foods (bananas and cheese) so that her future BM's would be just as easy.