I just can't make any sense of it 
It's already hard enough to understand Kirk letting Capt(or Major according the credits) Christopher access to the ship. I guess I can accept Kirks momentary lapse of judgement perhaps as the after effects of the black star(and the needs of the plot). I'm even willing to accept that Bones couldn't concoct some 23rd century roofies to confuse all Christophers memories.
But how can the ending make any possible sense.
Option 1. As the travel through time everything seems to return to its "in time" state. Hence beaming Christopher back into his own body as if nothing happened. This sorta explains the absence of the other Enterprise because there is somehow only one now...err the one flying around.....maybe? But if Christopher loses his memory why doesn't Kirk and co. ? I think this is what the writer was going for but I can't wrap my head around how it is supposed to work.
Option 2. Alternate timeline version. Kirk was full of crap and they just killed Christopher. Still doesn't make sense to me. They clearly didn't travel further back than the Enterprises original arrival in this timeline. Christopher is only even in the plane to intercept the Enterprise. It has to exist in this timeline also but where is it? Why does it vanish?

It's already hard enough to understand Kirk letting Capt(or Major according the credits) Christopher access to the ship. I guess I can accept Kirks momentary lapse of judgement perhaps as the after effects of the black star(and the needs of the plot). I'm even willing to accept that Bones couldn't concoct some 23rd century roofies to confuse all Christophers memories.
But how can the ending make any possible sense.
Option 1. As the travel through time everything seems to return to its "in time" state. Hence beaming Christopher back into his own body as if nothing happened. This sorta explains the absence of the other Enterprise because there is somehow only one now...err the one flying around.....maybe? But if Christopher loses his memory why doesn't Kirk and co. ? I think this is what the writer was going for but I can't wrap my head around how it is supposed to work.
Option 2. Alternate timeline version. Kirk was full of crap and they just killed Christopher. Still doesn't make sense to me. They clearly didn't travel further back than the Enterprises original arrival in this timeline. Christopher is only even in the plane to intercept the Enterprise. It has to exist in this timeline also but where is it? Why does it vanish?