Can mom keep her Medicare and Medicaid benefits if she moves from California to Florida?

Medicare is a nationwide federal entitlement program for those over 65. Once you apply, the card & policy # for it stay the same for Medicare A & B.

BUT Medicare part D varies by state.

Medicaid is a joint federal and state program and Medicaid is adminstered by each state. Each state has their guidelines similar yet different and depends a lot of each state's law. She would need to apply to Medicaid in the new state when she moves. She would need to do things to establish her residency in the new state - like change her state issued ID, get a bank account with an address in the new state, etc.

I would call the Agency on Aging in your area to ask how to do this. Lots of seniors move to Florida so the system for Florida should be pretty straightforward.