Since many of the above responses are wrong, you might just pull up the Medicare and You publication on line and read it. It may be long but it is very understandable.
The wording of your question implies, no states, that you are looking for supplemental or gap coverage under Traditional Medicare - not under one of the all inclusive Part C plans (those are the ones that may have geographic restrictions). Traditional Medicare is accepted throughout the country by every provider that accepts Medicare - no geographic restrictions. Under Traditional Medicare you can buy private supplemental plans (the alphabet plans SCBWR refers to), also called medigap plan. All supplemental plan C's for example will be identical with the only difference amongst those offering it being price and quality of service. All B's will be identical, all F's will be identical etc. ALL supplemental plans through all carriers must be accepted by all medicare providers. The only thing geographical about these plans is pricing and availability. For example, insurer #1 may offer a Plan B at $x per month in State A, County A but at a different price in State A, County B. That insurer might not even offer the Plan in County C.
So read the material, understand what the various Plans (Plan = supplemental while Part = type of underlying Medicare coverage) cover, review past actual medical history and forecast what you might need in the upcoming year and based on that forecast, pick the Plan that provides the best coverage value to you. Then, since you will be full timing and presumably picking a domicile state & county, check and see if that Plan is offered in your new county. If it is, you can use the Medicare online site to see what companies offer that Plan in your new area and pick the least expensive (no reason to pay more since the coverage is identical and the quality of service basically affects the medical provider (speed of payment etc), not you. It's an easy system if you take the time to learn it. It's an extremely difficult system to learn if a) you don't use and understand the correct terminology and b) you get advice from anywhere, including me, other than Medicare --- and the Medicare and You booklet is one of the better written ones in the panoply of government publications. JMO
The answer then to the question posed by your title is an unequivocal "yes" (by law).
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