The 15:50 flight departs from T4S, not from T4. You therefore have to take the bus from the jetbridge across to T4S (bypassing immigration), or go into the terminal, clear immigration (very short), walk down to the middle of T4, take the train across, clear immigration and go to the gate. Again, doable if on time, but you have to allow at least 25 minutes for the transfer, 15-20 minutes before departure to board, and give yourself 5-10mins from arriving at the gate to getting off the aircraft.

With having to recheck baggage, pretty much impossible - you'd have to check it in by 14:55.