HS25 FLC CHALLENGE L30 CTLR WHEN HDG CAUSES TCASII MANEUVER.

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LYNNS 1 ARR FROM PGS TRANSITION. ISSUED CLRNC TO DSND VIA STAR LAS. LEVEL 12000 FT LYNNS; TURNING R PER FMS TO MIROT TO CROSS AT 11000 FT. TFC WAS DEPICTED ON TCASII 700 FT LOW. CTLR ISSUED A DSCNT; 'EXPEDITE OUT OF 10000 FT FOR 8000 FT.' MOMENTS LATER; CTLR ISSUED US A TURN TO 020 DEGS INTO TFC WITH ALREADY AN EXPECTED DSCNT. BECAME A TCASII ALERT; FOLLOWED BY RA 'DSND; DSND; MONITOR VERT SPD.' TCASII INDICATED CLB TO MISS CONFLICT OF TFC. INITIATED A CLB TO 11000 FT; HDG 020 DEGS. CTLR STATED; 'YOU CLBED BACK ABOVE TFC AND YOU SHOULD BE ON 340 DEG HDG.' 'NO; WE WERE ISSUED 020 DEG HDG.' NO FURTHER PROB. LANDED LAS. CALLED LAS TRACON AND SPOKE TO THE CTLR AND ASKED HIM WHAT THE CONFUSION WAS. BASICALLY STATED BEING A LONG DAY WITH 2 HRS LEFT TO GO. THERE WAS NO PROB AND ASKED ME IF WE WERE GOING TO PURSUE THIS MATTER. I SAID NO; JUST WANT TO MAKE SURE EVERYTHING IS 'OK' -- NO VIOLATIONS OR INSTANCE FILED. HE INFORMED; 'NO; NOT UNLESS YOU WANT TO.' I SAID NO. THEN ASKED ME IF I WOULD FILE A NASA RPT. I TOLD HIM 'NO; BUT IF YOU WOULD LIKE ME TO; I WOULD.' TOLD ME TO HAVE A NICE DAY AND NOT TO WORRY ABOUT ANYTHING. CHAIN OF EVENTS I BELIEVE WERE THE EXPEDITIOUS DSCNT ASKED BY APCH AND A TURN INTO TFC.