Is it possible to transfer Pokemon from one Pokemon X/Y game to another if they know an HM move?
Can you make it forget an HM move if not?
No (at least not with all HMs).
I believe for HMs like surf, you can't do this (as then you would be able to access places you shouldn't be able to access). If you want to forget a move, use the Move Deleter in Dendemille Town. He will be able to not only forget moves on a pokemon, but also HMs.
put the pokemon with the HM move into a box, and then you can trade it over to your heart's content. Just traded all three starters (Froakie knowing Surf) Ghastly, Raltz, and Aerodactyl (with Fly) all from my X cartridge to my Y cartridge. The X is at postgame status whereas my Y cartridge has only gotten the first gym badge
Yes you can.
In generation 5 they added the feature to trade outside of a Pokemon Center and they made it so you can't trade any Pokemon from your party that have an HM. (To prevent you from getting stuck somewhere outside).
In generation 6 it's impossible to trade via the Pokemon Center so they kept the safety check for the Pokemon in your party but it's still possible to trade Pokemon with an HM that are stored in your PC.
Reason: Because trading can be done anywhere, trading a pokemon with an HM move could ruin a game. You could get stuck behind a boulder, rock, on an island or underwater. Seriously, trading your pokemon that knows dive while underwater. You'll be stuck forever! Also odds are the dive pokemon is the same as your surf pokemon. You'll have to start swimming. You can't trade ones in the PC because of balancing purposes. If you can't in your party, why should you be able to in your PC?