Rinse and drain the plums. Halve them and remove the stone. Cut the plum halves in half once more, this will give you quartered plums.
Place the plum quarters in a large, wide saucepan. Pour a little water over them; about a quarter of a cup is enough.
Turn the stove on to medium-high heat and cover with a lid. Soon the plums will start cooking. The added water will encourage the fresh fruit to release its juices and not burn.
Reduce the heat to low, remove the lid, and allow the plums to simmer until they form a thick liquid sauce with fruit chunks. This will take approximately 20 minutes. From time to time, give it a good stir with a long-handled wooden spoon.
Add sugar and stir well once the plums are soft and swimming in the juices.
Cook for another 20 minutes. The liquid will evaporate, and the klevela will thicken slightly, but the fruit pieces will remain visible.
Stir in the rum with the fruit.
Prepare jars with screw caps. Wash them thoroughly in the dishwasher or by hand in hot soapy water. Rinse the jars well and set them aside to dry.
Using a ladle, carefully pour the hot plum mixture into clean, still warm jars. Wipe the rim of the jar to keep it clean. Place the jar's lid on top, tighten it, and turn it upside down. Leave to cool completely.