Scoop the flesh from the figs with a spoon and discard the peels. Bring sugar and water to a boil in a large saucepan over medium-high heat, stirring until sugar has dissolved. Stir in fig pulp, lime juice, cinnamon, ginger, and white pepper. Cook, stirring often, until a candy thermometer reads 210 degrees F (100 degrees C), about 20 minutes.
While preserves are cooking, sterilize jar and lid in boiling water for at least 5 minutes. Pack the hot preserves into the sterilized jar to within 1/4 inch of the top. Top the jar with the sterilized lid and let cool before storing preserves in the refrigerator.