Ok never mind.... Mainland is just a quick phone call??? Don't we have FBI on the island that they can call?
On the mainland, the FFL dealer calls a 1-800 number for a quick background check, called a NICS (National Instant criminal background Check System) check. Some states have laws where if you present a Concealed Carry permit/license issued in that state, that NICS check isn't needed.
In Hawaii, they fingerprint you the first time, send it to the FBI for possible matches, then conduct their own background check during the 14 day period for your permit. This is done in lieu of the quick NICS check.
Next time you buy a gun, watch as the dealer fills out the federal paperwork (infamously known as the ATF Form 4473). There's a section where he needs to answer questions about the NICS check he's supposed to perform. There's a box he'll enter information in saying the NICS check wasn't needed because the state already conducted a background check. He'll then enter your Permit to Acquire information (Permit serial number, date of issue, date of expiry, etc.). On the mainland, when they use a CCW permit/license in lieu of a NICS check, they do the same thing, entering the CCW permit/license information.