To make the simple syrup combine all ingredients in a small saucepan. Bring to a boil and let simmer for 2-3 minutes.
Remove from heat, cover, and let steep for 30 minutes.
Pick out the large pieces of plum and dispose of them. Pour the remaining plum ginger syrup into a clean mason jar and store in the refrigerator for up to 2 weeks.
To make the mojito pout the rum, lime juice, and mint into a tall glass. Muddle together to combine the flavors.
Add in the plum ginger syrup.
Fill the glass with ice and then fill to the top with sparkling water. Mix well and serve.