ACR MLG TOOK COMPANY ACFT DSCNT CLRNC AND HAD LTSS WITH AN OPPOSITE DIRECTION ACR ACFT THAT WAS BELOW HIM. CONFLICT ALERT AND TCASII ACTIVATED.

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ACR ABC X AND ACR ABD BOTH WERE ON ZID'S FREQ 134.67 (HIGH SIDE). CTLR TRANSFERRED ACR ABD TO 121.32. ACR ABC X TOOK THE FREQ CHANGE. ACR ABC X CALLED ON 121.32. LOW SIDE CTLR (121.32) ACCEPTED AND AUTOMATED HDOF ON ACR ABD. LOW SIDE CTLR CLRED ACR ABD TO FL190. ACR ABC X READ BACK THE CLRNC. ACR ABC X DSNDED TO FL190 FROM FL350. AN ACR Y WAS WITHIN 5 MI OF THE ACR ABC X WHEN ACR ABC X LEFT FL350. BOTH VERT AND LATERAL SEPARATION WAS LOST. IN SUMMARY; TWICE ACR ABC X TOOK ACR ABD CLRNC. SUPPLEMENTAL INFO FROM ACN 261727: AT CRUISE OF FL350; WE RECEIVED A FREQ CHANGE TO ZID (122.22). I CHKED IN WITH ZID ON THE FREQ. ZID GAVE US A CLRNC TO DSND FROM FL350 TO FL190. WE STARTED A SLOW DSCNT DUE TO BEING ABOUT 140 NM FROM DAY. IMMEDIATELY; SOMEONE CAME ON FREQ AND REQUESTED WE RETURN TO PREVIOUS FREQ. AFTER CHKING IN WITH CTR; I ADVISED THEM OF OUR DSCNT CLRNC. CTR ADVISED THAT WE SHOULD RETURN TO FL350. AT THIS TIME; WE REVERSED DSCNT AT AROUND FL340 TO CLB TO FL350. WE RECEIVED A TA ALERT ON TFC AT FL330. NO EVASIVE ACTION REQUIRED; NO RA ALERT RECEIVED. CTLR APOLOGIZED AND HANDED US OFF TO ANOTHER ZID FREQ WHO ASKED US TO CALL UPON LNDG. WE CALLED AND LEFT A MESSAGE ON THE RECORDER. WE BELIEVE CTR GAVE INCORRECT CALL SIGN TO US IN THE FREQ TRANSFER. ZID MAY HAVE BELIEVED WE WERE ANOTHER ACFT IN CLRING US TO DSND.