Wash, drain and stone the plums. Then cut into fine strips and layer alternately in a bowl with jelly and vanilla sugar. Let it steep for 24 hours, turning or shaking occasionally.
The next day, bring the plums to the boil in a saucepan and cook for 4 minutes, stirring constantly, until foam forms. Just before filling into jam jars, add the rum. Close the jars and place on the lid for 5 minutes.