Wash the apricots, remove the stones and cut the plums into small pieces. Next, bring the apricot pieces to a boil along with the sugar, gelling sugar, lemon juice, cinnamon stick and the rum. Wait until the apricot pieces are soft. Use an immersion blender to pure them. The preserves are instantly ready for enjoyment and will stay fresh in the refrigerator for several weeks if filled into jam jars. You also have the option to sterilize the jam, which will extend its shelf life considerably.