B777 CREW UNDER EGPX (SCOTTISH ACC) CTL RECEIVE AND RESPOND TO A TCASII RA ABOUT THE SAME TIME THE CTR ISSUES A TURN TO AVOID XING TFC.

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WE WERE CLBING TO CRUISE ALT. WE BOTH NOTICED ANOTHER ACFT AT OUR CRUISE ALT. WE WERE CLBING TO THAT ALT. WE WERE JUST PICKING UP THE MIKE TO CALL ATC ABOUT TFC WHEN WE WERE GIVEN A L TURN. ABOUT THE SAME TIME; WE GOT AN RA TO CLB. THE CAPT TOOK THE ACFT OFF AUTOPLT AND DID EXACTLY AS REQUIRED BY THE RA. WE NEVER EVEN WENT THROUGH OUR CRUISE ALT. WE TOLD ATC WE HAD AN RA AND WERE THEN GIVEN TO PROCEED ON COURSE. NEVER HEARD ANOTHER WORD FROM ATC UNTIL TODAY. WE SAW THE PROB; WE COMPLIED WITH INSTRUCTIONS FROM ATC AND THEN COMPLIED WITH OUR RA. SUPPLEMENTAL INFO FROM ACN 617488: WHILE CLBING TO CLRED NAT XING ALT AND PROCEEDING DIRECT TO NAT GATEWAY; WE WERE GIVEN AN OFF COURSE HDG 'TO AVOID XING TFC.' FOLLOWED TCASII DIRECTIONS AND NOTIFIED SCOTTISH CTL AS SOON AS POSSIBLE. CALLBACK CONVERSATION WITH RPTR ON ACN 617489 REVEALED THE FOLLOWING INFO: RPTR STATED THE COMPANY CALLED THE PLTS FOR INFO CONCERNING THE INCIDENT. THE COMPANY HAD RECEIVED A CALL FROM THE ATC FACILITY AND WAS TOLD THE PROB WAS CAUSED BECAUSE OF CTLR TRAINING. THE RPTR SAID THEY WERE GIVEN A 15 DEG TURN L ABOUT THE SAME TIME A TCASII RA WAS RECEIVED REQUIRING A CLB. HE SAID THEY WERE NEBOUND AND IMMEDIATELY SAW A B737 BTWN 9 AND 10 O'CLOCK POS IN A SE DIRECTION XING BEHIND THEIR FLT. HE SAID THE B737 WAS AT LEAST 5 MI AWAY WHEN IT WAS SPOTTED.