Rinse cherries and currants in cold tap water. Let drain properly on a sieve. Remove berries from panicles with a fork. Remove stems and pits from cherries. Squeeze the juice. Blend cherries and berries in hand mixer until puree is fine. Pour into bowl. Add cherry juice. Gradually add sugar with a wooden spoon. When the sugar has dissolved, pour the jam into jars. After 12 h, place on each jar a round piece of parchment paper dipped in rum, of the same diameter as the jar.
Seal jars as directed.
Speaking of which, raw stirred jam like this should be used up after 3-4 months. It will keep longer in the freezer.