Can we bill an Admit & Discharge on Same Day /SNF?

A provider admits a patient to a skilled nursing facility in the AM.
The patient (at family's request) is discharged by the same physician
in the evening.

Can the provider bill an Admission on one claim and a Discharge code on another claim?

What is the proper billing format for this situation?

Hospital/NH

A hospital discharge code may paid in addition to a NF admission code on the same day (Medicare)

Hospital/NH

You may not bill an initial nursing home service, 99304-99306 and the nursing facility discharge on the same day, 99315-99316, There are no CPT codes for admit/discharge on the same calendar date for nursing facility, like there are for hospital.

If the admission is documented appropriately, bill the admit.