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There is no passport control at T5 when you are in transit from JFK to TXL as well as on your return.
However, you will have to pass BP compliance check (they check that you enter the departure area 35 mins or more prior to your flight.
You then clear airport security (expect long queues in the morning.
You only clear German immigration when you get to TXL. There is one desk per flight and the queues are short and fast!
You do not clear UK passport control unless you wish to exit the airport (for example to smoke)
You do not have to pick up your bags and re-check them in as you are flying through on BA.