As TD explained, it is quite common for members from one family, after relocating to another city in another state, to eventually "transfer" their memberships to the resident Family of the new state.

In fact, there is actually a rule (or was a rule,) that if you permanently move to the new state, you are required (by Cosa Nostra doctrine) to switch over after a six-month period.

Part-time guys, vacationers, temporary fellas living in another place....No! But if you move into that state permanently, it's required.

[But within the Five Families, that was extremely rare. It's only happened a few times.] Traditionally, you stay put within the Family you are "made" into...period!
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PS: Another steadfast rule, and one that was adamantly adhered to the letter, was that BEFORE you come into another territory to do business, whether illegal or legal, it was expected that the boss of your borgata notify and technically "ask permission" of the boss of the territory you're coming into, as a courtesy and to show respect.