For the banana jam, wash and clean blueberries. Peel bananas, chop them coarsely, sprinkle with lemon juice and leave to infuse for half an hour.
Put fruit together in a saucepan, pour water, add sugar, cinnamon and rum and cook for about 10 minutes, stirring, until the jam has developed the right consistency.
Pour the mixture into jam jars rinsed with hot water.