First place the pineapple pieces, ginger root, citrus zest and star anise into a large jar. Or divide the ingredeints between 2 wide mouth quart mason jars.
Once you have filled your container with all of the fruit, spices and citrus zest pour the entire 750 ml bottle of rum into the jar/jars. Cover the jar with a lid and shake the jar or you can also use a wooden spoon to mix the ingredients.
Place the jar in the refrigerator. Keep refrigerated for at least two weeks.
After two weeks pour the contents of the jar through a fine mesh strainer that has been placed over a large bowl.
Pour the infused rum into clean containers. Keep the Pineapple Ginger Rum refrigerated until ready to use.