B90 INSTRUCTOR AND STUDENT PLT STRIKE PROP ON A RWY SIGN AFTER LNDG IN A RAIN SHOWER.

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I WAS CFII ON AN INST TRAINING FLT TO FXE. ATIS FOR FXE RECORDED ABOUT 10 MINS BEFORE ARR WAS SCATTERED CLOUDS; 10 MI VISIBILITY; WINDS 120 DEGS AT 7 KTS. WHEN CLRED FOR ILS RWY 8 APCH; WE SAW THE END OF RWY 8 FROM AT LEAST 5 MI OUT. THERE WAS A RAIN SHOWER IN THE TOUCHDOWN ZONE AREA; BUT IT APPEARED LIGHT AND INNOCUOUS. TWR GAVE NO ALERTS ABOUT POTENTIAL PROBS WHEN THEY CLRED US TO LAND. ON SHORT FINAL; AT ABOUT 100 FT ABOVE TOUCHDOWN; RAIN BECAME MODERATE AND STUDENT WAS DRIFTING L AND I TOOK THE CTLS AT ABOUT 50 FT TO CORRECT BACK TOWARD THE CTR OF RWY. DURING FLARE; A STRONG XWIND DRIFTED US TO THE L EDGE OF THE RWY AND WE HAD INCIDENTAL PROP STRIKE DAMAGE WHEN THE PROP STRUCK A SIGN ON THE RWY L EDGE. I BELIEVE IT WAS A DISTANCE REMAINING MARKER. NO INJURIES WERE SUSTAINED. I THINK THERE WAS SOME 'DOWNBURST' ASPECT TO THIS SEEMINGLY 'SMALL RAIN SHOWER.' WE WERE NOT ALERTED BY THE TWR OF ANY CHANGE IN WIND; BUT I BELIEVE THERE WAS A LOT STRONGER AND GUSTY XWIND THAN RPTED BY ATIS OR TWR. ALSO; ALTHOUGH WE WERE MUCH FARTHER L ON THE RWY THAN WE SHOULD HAVE BEEN; WE WERE STILL ON A 'HARD SURFACE' RWY EDGE. RWY SIGNAGE SHOULD NOT BE ON THE HARD SURFACE PART OF THE RWY. IT SEEMS IT SHOULD BE IN THE GRASS.