Wash the currants and put them in a saucepan as they are. Turn the stove to the highest setting and bring the berries to the boil until they slowly lose their juice. Then press it through a sieve, catching the juice. Use only the juice. Put this in a fresh saucepan.
Bring to the boil together with the preserving sugar, coconut milk and (a really good shot) rum.
Note: It may be necessary to measure again while mixing, whether the amount without sugar is around 900 - 1000 ml - if in doubt, it is better to add a little less, then just add less coconut milk.
When the mixture boils, let it cook for at least another 4 minutes. Then make a gelling test (on a plate).
Pour into clean jam jars that have been washed out with hot water. Seal and turn upside down for 5 minutes. Then let it set until at least the next day.