Step 1In a heat-proof measuring cup, combine the sugar with 3 tablespoons water, stirring to combine. Heat on medium heat in a microwave for 30 seconds. Or place the sugar and water in a heatproof bowl and set the bowl on top of a small saucepan filled halfway with boiling water, stirring just until the sugar melts and forms a syrup, about 20 seconds. Remove from heat and allow to cool slightly.
Step 2In a cocktail shaker, combine the ginger and lemon juice. Using a muddler or the back of a spoon, mash the ginger well. Add the syrup and strain into a glass or plastic bowl. Cover and refrigerate up to 5 days. Makes 2 1/2 ounces.
Step 1In a cocktail shaker, combine the rum, Elixir G (or ginger-lemon syrup), pineapple juice and orange juice. Fill with ice and shake until chilled. Strain into an ice-filled cocktail glass. Top with ginger beer.