TFC CONFLICT NEAR JACKSON; MS. TCASII NOT FOLLOWED IN PREFERENCE TO SEE AND AVOID.

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WE WERE HANDED OFF FROM ZMP TO JACKSON APCH. WE WERE DSNDING OUT OF ABOUT 14000 FT. AROUND 7000 FT WE WERE TURNED BY APCH TO A 250 DEG HDG. SHORTLY HE TURNED US TO 270 DEGS AND CALLED TFC AT 12:30 O'CLOCK POS AND 3 NM. AT 5200 FT WE WERE DSNDING AT 2500 FPM; AT THAT POINT APCH ASKED US TO MAINTAIN 5000 FT. BY THEN WE WERE ALREADY TAKING EVASIVE ACTION. WE WERE NOT ABLE TO MAINTAIN CLRNC BECAUSE OF OUR TCASII ADVISORY ALERT. WE SAW THE TFC COMING AT US ON OUR TCASII. HE WAS ABOVE OUR ALT; BUT DSNDING RAPIDLY AT US; SO WE INCREASED OUR DSCNT RATE AS ADVISED BY TCASII. ONCE WE REALIZED WE WERE NOT GOING TO BE ABLE TO MEET TCASII REQUIREMENT TO TURN AND DSND; WE LEVELED OFF OR SLOWED DSCNT AND AIRSPD AS RAPIDLY AS POSSIBLE TO AVOID ANY FURTHER CONFLICT. THE LEARJET THEN PASSED R TO L IN FRONT OF US AT OUR ALT WITHIN 6000 FT TO 3000 FT. THERE WAS NOTHING ELSE WE COULD DO. WE INFORMED THE CTLR AND HE ADMITTED TO MAKING THE MISTAKE. I HAVE NO COMMENT ON A CORRECTIVE ACTION. THE PF AND MYSELF WERE ALERT AND VIGILANT. I CANNOT SPEAK ON BEHALF OF THE CTLR. HAD IT NOT BEEN FOR TCASII A COLLISION MIGHT HAVE OCCURRED.