Here was my recent experience at HPD back in July. I've had many registrations before then (all good, no problems), but this one might give you some perspective on how HPD does business.
My father had passed away in June from cancer and I brought back from California a number of long arms and pistols to register. My mom was the executor of his estate, and as per the HPD information on their website, we got a notarized form showing the transfer of the firearms to me. I also had a copy of his death certificate. When I went up to the counter they didn't want to see any of the paperwork, they just believed me when I told them and processed it as an out-of-state registration. While I was waiting for my paperwork to be completed, I watched a guy attempt to register his Dad's shotgun, which he thought wasn't registered. His Dad had died locally 15 years ago, and the guy trying to register it never did anything with the shotgun. Turns out the shotgun was registered with his Dad. HPD demanded to see proof of his death certificate and a notarized form saying that the son was the executor of his Dad's estate before they would process the registration (the same thing they said they didn't need from me, despite the guidelines on the HPD website). The man had zero paperwork, his excuse was that they didn't know about the transfer requirement and his Dad never told him about how to care of his final arrangements. The guy at the counter was having none of it - told the man to come back within 10 days with the proper paperwork or they would confiscate and destroy the shotgun. Whether that was bluster on his part or not I don't know, but it certainly had the desired impact.
Bottomline, the guys at HPD have limited discretion. Follow the law as per the HRS 134 series, and you will have no problems. If you have any questions, call the HPD Firearms section and ask. They were very helpful and answered all my questions when I was still in CA and about to fly back with the firearms.