What's the best way to handle this?

NFA items are purchased and are held by a corp in state A.

A 5320 is approved to permanently move those NFA items to state B, but the corp that owns them is still in state A.

This is existing NFA, not new stuff.

Is it better/easier to maintain the corporation in state A as the owner?

- Can that be done without a physical address there? - file for Foreign Authority?
- How would a transfer of the corp to state B affect the NFA status assuming it's the same name, same corp?

Thanks for any direction you can lend.

This sounds like the sort of thing you need to discuss with a lawyer and not a bunch of dudes on the internet.

You're going to have to naturalize a foreign corporation.  Each state has different laws for that.

Seek out a lawyer in the new state.