Facility Transfer New vs. Established

There is a debate going on between me and my doctor, and I need help ending it. My doc is a hospitalist and sees patients in hospitals and in SNFs. So s/he will sometimes follow a patient from facility to facility.

Scenario #1: If a patient was seen in a hospital as a new patient, then transfer to a SNF, is this a New or Established Patient at the SNF?

Scenario #2: If a patient was seen in Hospital A, and then transfer to Hospital B. Is this a New or Established Patient at Hospital B?

I believe in both scenarios that the patient is established due to decision tree. If he was the admitting physician in Scenario #2, then I know that it would be initial, but if he's not admitting does that mean that the patient is established?

Thanks for your help!!!

Facility Transfer New vs. Established