Stone the plums and place in a sufficiently high saucepan. Puree the fruits to the desired consistency. It doesn`t matter if some pieces of fruit remain visible. Now add the preserving sugar, star anise, cinnamon, the plum liqueur and lemon juice and mix everything together well. Put the lid on and leave it in a cool place overnight. The next day, slowly bring the plum mixture to the boil and let it simmer for about 4-5 minutes, stirring constantly. Every now and then skim off some foam. After the cooking time, remove the saucepan from the hot plate and season with rum. Immediately fill into hot rinsed glasses and turn them upside down for about 5 minutes.