ARTCC RADAR CTLR IN TRAINING CLRED A LR25 TO DSND TO FL310 AND TURN TO A 270 DEG HDG. ACFT READ BACK CORRECT HDG; BUT SAID DSND TO FL270. TRAINEE CTLR RECLRED ACFT DIRECT TLH AND DSND TO FL310; BUT THE ACFT DSNDED THROUGH FL310 FAR ENOUGH TO LOSE SEPARATION WITH AN ACR CL60 AT FL290.

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CL60 ACFT SBOUND AT FL290. LR25 ACFT NBOUND AT FL390. LR25 ACFT LNDG TLH SO DSCNT CLRNC ISSUED TO FL310 ALONG WITH A TURN TO 270 DEGS. LR25 READ BACK HDG 270 DEGS AND ALSO DSNDING TO FL270. R SIDE (TRAINING) RECLRED ACFT DIRECT TLH AND DSCNT TO FL310. THIS TIME LR25 READ BACK THE CLRNC CORRECTLY; DIRECT TLH AND DSNDING TO FL310. CONFLICT ALERT ACTIVATED AS LR25 DSNDS THROUGH FL310 AND R SIDE TOLD THE LR25 ABOUT THE SBOUND CL60 AT FL290. LR25 RPTED LEVEL AT FL310 JUST BEFORE SEPARATION WAS LOST. I THINK THE LR25 DIDN'T REALIZE THAT HE HAD BEEN GIVEN A NEW ALT; EVEN THOUGH THE LR25 READ BACK THE REVISED ALT. THERE WAS CTLR TRAINING ON THE R SIDE. THE R SIDE INSTRUCTOR CAUGHT THE FIRST READBACK ERROR; BUT THE TRAINEE DIDN'T. I WAS WORKING THE D-SIDE AND DIDN'T HEAR THE MISSED READBACK EITHER. INSTRUCTOR TOOK NO IMMEDIATE ACTION TO CORRECT THE WRONG READBACK BY THE LR25 PLT; BECAUSE THE TRAINEE JUST A FEW SECONDS LATER RECLRED THE ACFT DIRECT TLH AND REISSUED DSCNT TO FL310. LR25 DID READ BACK THIS CLRNC CORRECTLY.