RADAR CTLR IN TRAINING CLBED AN ACR B737 THROUGH THE ALT OF A KING AIR WITH LTSS. THE INSTRUCTOR CTLR WAS BRIEFING HIS RELIEF AND DID NOT HEAR OR SEE THE TRAINEE ISSUE THE CLB CLRNC TO THE B737. THE CONFLICT ALERT ACTIVATED AND THE INSTRUCTOR CTLR HAD THE TRAINEE TURN THE KING AIR; BUT SEPARATION HAD ALREADY BEEN LOST.

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I; THE ON THE JOB TRAINING INSTRUCTOR; WAS GIVING TRAINING TO AN FPL TRANSFEREE ON RADAR POS OF COMBINED SECTOR. 6 OR 7 AIRPLANES ON FREQ. ACFT #1 CHKED ON FREQ CLBING TO FL230. I OBSERVED ACFT #2 IN VICINITY AT FL240. TRAINEE ROGERED ACFT #1 AND SAID I'LL GET BACK TO YOU SHORTLY. TRAINEE WENT ON TO OTHER DUTIES. WE WERE THEN ASKED IF WE WANTED TO BE RELIEVED FROM POS AND TAKE A BREAK. AT SOMETIME DURING THAT CONVERSATION WITH RELIEVING CTLR; TRAINEE CLBED ACFT #1 TO FL270. NEITHER MYSELF NOR MY RELIEF HEARD TRAINEE ISSUE CLRNC TO CLB. TRAINEE CALLED TFC TO ACFT #2 WHO RESPONDED TFC IN SIGHT. WHEN I FIGURED OUT WHAT WAS GOING ON I INSTRUCTED TRAINEE TO TURN ACFT #2 S OR 60 DEGS L; BUT ACFT #1 AND #2 WERE ALREADY LTSS WITH CONFLICT ALERT ACTIVATED. TRAINEE'S INACTION OR LACK OF AWARENESS WAS PARTLY DUE TO COMING FROM A TERMINAL ENVIRONMENT TO A CTR ENVIRONMENT. IE: TFC PERFORMANCE; STRIP MARKING; COMPUTER ENTRIES. SINCE I HAD NOT ISSUED OR HEARD CLRNC GIVEN; I WAS UNAWARE OF POTENTIAL SIT EXCEPT FOR THE FACT THAT I OBSERVED ACFT #1 CLBING AND BEING ROGERED TO FL230 AND ACFT #2 IN VICINITY. MY SLOWNESS IN ACTION WAS DUE TO MY DISTANCE FROM RADAR SCOPE (HAVING MOVED AWAY FROM SCOPE TO LET RELIEVING CTLR IN) AND NOT BEING ABLE TO DETERMINE POS OF ACFT SO AS TO ISSUE CLRNCS TO SEPARATE THE 2 AIRPLANES WITH VECTORS OR ALT ASSIGNMENTS.