Long guns - no problem.
Unless they meet NY state's definition of an assault rifle. He should check here if he does have one that fits the criteria, and what he should do about it. http://programs.governor.ny.gov/nysafeact/gun-owners
Pistols - NYS does not have reciprocity with other states. He can start looking at how/where to check about getting a pistol permit here. http://www.ny.gov/services/how-obtain-firearms-license
Then he'll have to check with and go through whatever county he winds up in because the permits are done at the county level.
And, advise him that he'll be moving to a state that requires a back ground check just to buy ammo, and no direct internet buying ammo allowed here ! It has to be done through an FFL.