Remove the furry skin from the quince, peel and cut into pieces. Boil 1 kg of it with a little water until soft. Then process into a fine purée with a hand strainer and strain through a sieve.
Put the quince puree in a saucepan and bring to the boil with the sugar, cinnamon and lemon juice for approx. 5 minutes. Be careful, it can splash. Shortly before the end of the cooking time, add the rum (approx. 2 cl or more, depending on your taste) and pour it into the prepared glasses while hot.