A CE550 FLC RPTS THAT WHILE FLYING AN APCH OWN NAV; THAT AN ACFT THEY HAD VISUAL CONTACT WITH EXPERIENCED A TCASII.

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WE CONTACTED APCH; AND AFTER RADAR CONTACT; WE WERE GIVEN VECTORS FOR THE ILS RWY 13 INTO HUT. WE WERE GIVEN A 270 DEG VECTOR AND MAINTAINED 3500 FT MSL. APCH WAS ALSO IN COM WITH A BEECH JET THAT HAD BEEN GIVEN INSTRUCTIONS TO HOLD OVER SALTT INTXN. SALTT IS THE FAF FOR THE ILS RWY 13. SINCE WE UNDERSTOOD THAT THE BEECH JET WOULD BE DOING MULTIPLE TURNS IN THE HOLD AT 4000 FT; WE REQUESTED TO PROCEED UNDER OUR OWN NAV FOR THE STRAIGHT-IN ILS RWY 13 AT 3500 FT. DUE TO THE VECTOR; WE WERE POSITIONED W OF THE FACILITY. WE WERE CLRED TO PROCEED; OWN NAV; FOR THE ILS RWY 13 WITH NO SEPARATION SVCS PROVIDED. WE MADE A L TURN AND PROCEEDED TOWARDS THE FAF WITH THE INTENT TO PROCEED STRAIGHT IN. AS WE PROCEEDED TOWARDS THE FAF; WE MADE VISUAL CONTACT WITH THE BEECHJET; WHO WAS ON A CONVERGING PATH WITH OURS. THE BEECHJET WAS AT A HIGHER ALT THAN OURS; AND WE APPEARED TO BE APCHING THE FAF AT A GREATER RATE OF SPD THAN THE OTHER ACFT. AT NO TIME DID WE LOSE SIGHT OF THE OTHER ACFT; NOR DID WE FEEL IT WAS NECESSARY TO MAKE ANY DEV FROM OUR COURSE/ALT TO AVOID A TFC CONFLICT. THE OTHER ACFT RPTED RECEIVING A TA DURING THIS INCIDENT.