"If he has Medicare, is he allowed to have an HSA?"

Yes. You can no longer contribute to it, but you can still have it and keep using it. You can research if your State allows a Medical Savings Account (which is not the same as FSA or Medicare savings), and it works nearly the same, but contributions are not Fed deductible. And there is at least one High Deductible Medicare supplemental plan (Medi-Gap) (don't know if it is in every market), but you still can't contribute to HSA with this option.

The $1,000 make up amount is triggered at 55.