Place sugar, water and ginger in a small  saucepan and bring to a   boil. Reduce heat to a simmer & cook until  liquid is clear and   thickened slightly, about 5 minutes.

Remove  from heat and let cool completely. Strain syrup through a   fine-meshed  sieve, pressing down on ginger to extract all flavor &   syrup.  Discard ginger.

Place pineapple, mango, ¼ cup of the ginger  syrup, lime juice and   zest, rum and mint in a bowl and toss to combine.  If desired, chill   before serving.