As long as the item in question is legal in the destination jurisdiction, you only need to have an approved 5320.20. It's important to ensure that there are no local and/or state laws that prohibit the possession or use of the item in question. An approved 5320.20 is NOT A FREE PASS. ATF can, and has, made mistakes on approving 5320.20 to jurisdictions where the item is not legal.
An interesting note -- you can put a 5320.20 in for an entire year. I have submitted multiple 5320.20s for my entire collection. You need to have a different form for each destination (state).
If you happen to be an FFL/SOT, you do not need the 5320.20.