LESS THAN STANDARD SEPARATION BETWEEN 2 IFR CORP ACFT. OPERATIONAL ERROR.

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AT XA52 CORP X MADE INITIAL CALL TO WICHITA APCH CTL W. HE WAS LEVEL AT 10000' MSL AND 2-3 MI NW OF HUTCHINSON VORTAC. I INSTRUCTED HIM TO DSND AT PLT'S DISCRETION; MAINTAIN 7000'; EXPECT VECTORS ILS 19R APCH. I DID NOT OBSERVE ANY TARGET/MODE C WHICH MIGHT BE A CONFLICT. AT XA53 ZKC CALLED AND TOLD ME NOT TO DSND CORP X BELOW 9000' BECAUSE HE HAD XING TFC Y AT 8000'. AT THIS TIME X WAS ALREADY DSNDING THROUGH 8200'. I REQUESTED A TURN AWAY FROM TFC; WHICH WAS APPROVED. TFC WAS ISSUED; NOT SEEN; AND SEP WAS LOST. CONTRIBUTING FACTORS: COM ON CORP X SHOULD NOT HAVE BEEN TRANSFERRED TO ME UNTIL CONFLICT WAS RESOLVED. A NEW LETTER OF AGREEMENT HAD BEEN IN EFFECT ONLY 2 WKS. I DID NOT REALIZE THAT ACCORDING TO THE NEW LOA; I WAS NOT ALLOWED TO DSND ARRS UNTIL THEY ARE WITHIN 10 MI OF ICT BOUNDARY. I DSNDED CORP X 4-5 MI TOO SOON ACCORDING TO THE LOA; ALTHOUGH A LOSS OF SEP STILL PROBABLY WOULD HAVE OCCURRED IF I WAITED UNTIL THE 10 MI MARK. EITHER WAY 7110.65 PAR 5-64C WAS NOT COMPLIED WITH BY THE TRANSFERRING CTLR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: RPTR GAVE ATC EXPERIENCE; TYPE ACFT FOR Y; LOCATION OF AIRSPACE BOUNDARY BETWEEN ICT AND ZKC IN THAT AREA; AND MISS DISTANCES AT CLOSEST POINT. WHEN 1 MI LAT ACFT X WAS 400' BELOW ACFT Y. REVIEW BOARD SAID PRIMARY CAUSAL FACTOR WAS HER FAILURE TO COMPLY WITH LOA AND PREMATURE DSCNT TO X. ICT HAS ARTS II AND ASR 7. RPTR IS STILL A DEVELOPMENTAL; BUT WAS CERTIFIED ON APCH CTL W AT TIME OF INCIDENT.