if he legally remains a CT resident, in order to transfer/sell the handgun to him he will need to have a CT pistol permit and use the standard procedure of calling DPS for an authorization number and filling out the dps-3 forms and filing with the town and dps. How far along in the application process is he? there is no reason why he can't finish the process. even if he establishes residency in another state, he can still aquire his CT pistol permit. the permit just needs to have the most current legal residence address even if it's an out of state address.
he is able to "borrow" the gun on his travels without issue. and just to be sure (not necessary, but may help him if an officer questions his possession of it); you and him could sign a paper that you create saying that you are allowing him to borrow the gun, and include the serial number and description, and your contact information. this way if he ever has police contact for whatever reason and they ask who's gun it is, he can tell the truth (you let him borrow it) and show them the paper, and they can call you to verify
the most important factor in all this though is that he needs to make sure he abides by all laws in whatever state he is in at the time. and in CT he is not legally allowed to transport the gun anywhere even locked in the trunk and unloaded because he doesn't have his CT pistol permit. (this is a questionable law though, because there are laws about transporting a legally owned firearm in/through CT by out of staters).
I don't know many laws for other states, but in NY you can't even have a handgun in your own house unless you have a NY pistol permit. so it would simply be his duty to research the laws in whatever state he is in at the time to make sure he follows the laws. and some states don't require a permit at all.
this is just one more stupid thing about CT laws; you do not need to have a CT pistol permit to own a handgun or to possess it inside your house including carrying it on your person inside your house. but you do need a permit to buy a gun