You can suggest she develop a nightly routine (bath, p.j.’s, reading time, etc) but if she’s not willing to take your suggestions, I don’t think there’s much you can do about it.

Otherwise, just let him rest his head on the desk/table when he is tired. He may miss some of the class work, but at least you can work with the others. When his mom asks about the work you tell her that he was so tired he couldn’t do it. He is only four, so he doesn’t have to be in school yet anyway. Perhaps she could put him in a different program.

You can not even be sure that he is going to bed at 9 each night. Maybe that is just what the mom wants you to believe. Perhaps other stuff is going on at home that has him upset and not resting. You may never know exactly what is causing it. You have told the mom and she is aware of the problem, so there is not much more you can do unless she is willing to do what she can to help him.