I think the key thing you mention here is that he does not do all of his homework.
That’s not unusual at all. I literally listened to a dean of admissions at very good college mention this very thing recently.
She was just giving your student a bit of transparency about what she would say in case he wanted to ask another teacher where he might have turned in all of his work.
As far as what to do, do the colleges he is applying to ask for a STEM rec? Is there a science teacher he could ask in a class where he has turned in his hw? If yes, ask that teacher. If not, use the calc teacher’s rec.
He should only wait and ask the next math teacher if he plans to turn the hw in. Otherwise, the letter from that teacher might say the same thing.