SMA ON FINAL APCH TAKES EVASIVE ACTION TO AVOID SECOND ACFT ON FINAL.

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I WAS ANGLING INTO RWY 15 AS INSTRUCTED BY ATC. AS I WAS TURNING A HALF MI FINAL; MY STUDENT (IN THE L SEAT; BUT I WAS FLYING) LOOKED AT OUR 4 O'CLOCK POS AND YELLED THAT AN AIRPLANE WAS THERE. I LOOKED AND SAW A TWIN HDG RIGHT FOR US. I ESTIMATE THAT 3 SECONDS LONGER AND WE WOULD HAVE HIT. IT WAS SO CLOSE I COULD ALMOST SEE THE PLT'S EYES BULGING OUT! ANYWAY; I PUT A HARD FGT LIKE; BANK INTO THE L AND CALLED 'FDI IS GOING AROUND.' IT'S HARD TO BELIEVE HE NEVER SAW US UNTIL AFTER OUR TURN. IT TURNS OUT THAT TWR WAS CALLING US BY 'FFH' INSTEAD; REF TO ANOTHER ACFT THAT WAS ALSO IN THE ATA. SO HERE FFH WAS DOING 360'S AND WHAT HAVE YOU EVEN THOUGH HE WAS QUITE A WAYS OUT. I'M GLAD THAT I'M ABLE TO EVEN SIT DOWN AND WRITE THIS -- CLOSEST CALL I EVER THOUGHT I'VE HAVE. WHAT COULD I HAVE DONE TO PREVENT THIS? NOT GO FLYING THAT DAY. SERIOUSLY; I DON'T KNOW. GIVEN THAT I WAS CLRED TO LAND AND DOING EVERYTHING PER TWR'S INSTRUCTIONS -- AND ALSO KEEPING OUT A FORWARD SCAN; IT'S HARD TO SAY. I'M AMAZED MY STUDENT HAPPENED TO BE LOOKING OUT AT A 4 O'CLOCK POS AS WE TURNED FINAL.