I must add my Kudos.. I'm quite pleasantly surprised at how well you have managed to combine both stories. I find that the way you managed to transition from HP to ST:TOS quite believable, unlike some FanFic's where the transition is done in a far fetched way, using obscure "Magic's" as an explanation .  
You have managed to keep the characters pretty well in character, allowing them room to adapt. 
Looking forward to the next exciting chapter... 
Thanks for your time and effort.