According to feek61’s memo, there were only 4 practical or hero P1 and P2 phasers. HeroComm has done an outstanding job of documenting and screen matching 4 phasers. No more, no less. That’s pretty solid backing for the Feek61 memo. So it follows that any authentic Phaser must be one of the 4.
It's like the move Clue, there are a couple ways this could have happened, and the Phaser could be an authentic hero.
I’ll talk about the P1 first, and only in regards to the timeline. No attempt is being made to account for it's appeareance. According to the HA description, the P1 was acquired by a member of the production crew after filming completed on a second season episode in 1967. Assignment Earth, which has 2 screen matched phasers, the Finny/TMOST and the Nona, was filmed in early 1968. Supposedly, the P1 left the set before that, so the only documented P1 left is the P1 Four, Lenore.
In order for the HA P1 to be authentic, and screen used, it must be Lenore, so how to explain the appearance? After Lenore’s appearances in Episode 1x12 “The Conscience of the King” and being used in Episode 1x13 “The Galileo Seven”, the ruby watch crown was removed, it was painted with a heavy hand, and Velcro was added. This would have to happen after the original Chang refit, and before it disappeared from set sometime in Season 2. Then it disappears for 50 years, from mind and memory, only to be reunited with a P2. The only part of this story that troubles me is the chain of custody from the set to the auction house, and why it shows up now. That, in all honesty, is not a big deal, if everything checks out.
So if the HA P1 is Lenore, the TV appearance timeline seems to check out. The only rub is explaining the alteration of appearance from how it appeared on screen, and screen matching it. The possibility of it going back to Chang's shop for repair along with the P2 before Chang left seems to work out, or it could have been repaired/repainted by someone else. I don't know enough to make any determination there. It's subsequent lack of appearances later in the series makes sense if a crewmember absconded with it.
I’ll need to do some more research on the P2, as I’m even less familiar with that those.