A320 CREW CLBING OUT FROM FLL TAKE EVASIVE ACTION AFTER RECEIVING A TCASII RA TO DSND. INTRUDER ACFT SPOTTED AT 9500 FT WITH ATC HELP.

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AT 8800 FT CLBING TO 15000 FT; GOT TCASII RA TO DSND; DSND NOW. HAD JUST SEEN TARGET ON TCASII BEFORE WARNING. WAS IN A L TURN TO 280 DEGS PER ATC -- STARTED DSCNT AND ADVISED ATC. CTLR SAID OH; YES; THERE HE IS; TURN R 10 DEGS. WE DID THAT AND SAW TFC VISUALLY AT 9500 FT AND SEVERAL MI FROM US. HAD WE NOT GOTTEN RA; WE WOULD HAVE LOST SEPARATION. NO OTHER PROBS. RETURNED TO 280 DEG COURSE PER ATC; AND REMAINDER OF FLT WAS UNEVENTFUL. SUPPLEMENTAL 579830: ON DEP DURING CLBOUT; WE WERE ON A 320 DEG HDG (I BELIEVE); AND CLRED TO CLB TO AN ALT ABOVE 10000 FT. WE WERE THEN ISSUED THE FOLLOWING CLRNC: 'TURN L HDG 280 DEGS JOIN THNDR TRANSITION.' AS I TURNED THE ACFT THROUGH A HDG OF ABOUT 300 DEGS AND AN ALT OF ABOUT 8800 FT; WE GOT A TA FROM TCASII. A TARGET WAS TO THE L OF US 500 FT ABOVE US. I IMMEDIATELY ROLLED OUT OF THE TURN. AT THE SAME TIME; THE TA TURNED INTO A RA. THE VERT SPD INDICATED A COMMANDED DSCNT OF ABOUT 2000 FPM DOWN (WAS HARD TO READ WITH THE SUN SHINING ON THE PFD). I ROLLED THE ACFT TO THE R WHILE SIMULTANEOUSLY LOWERING THE NOSE FROM ABOUT 10 DEGS UP TO ADHERE TO THE RA. AS THE NOSE WENT DOWN; THE AIRSPD WENT UP (FMA WAS STILL 'THRUST CLB; OPEN CLB'); AND I THEN BROUGHT THE THROTTLES TO IDLE TO DISENGAGE THE AUTOTHROTTLES AND GET THE SPD UNDER CTL. MAX SPD WAS ABOUT 265 KTS WITHIN SECONDS WE GOT THE 'CLR OF CONFLICT' AND AFTER WE CLRED THE SIT WITH ATC; WE TURNED BACK TO A 280 DEG HDG AND JOINED THE TRANSITION. IT WAS CLR THAT ATC HAD NOT SEEN THE VFR TARGET PRIOR TO US POINTING IT OUT.