Steps

1. In a covered preserving pan — a wide, heavy, nonreactive pan (I use a big Le Creuset pot with sloping sides) — over medium heat, bring the currants and raspberries to a simmer. Uncover the pan, and simmer the fruits about 5 minutes, until they are quite tender (if you use fresh fruit instead of frozen, the simmering will take a bit longer).
2. Purée the mixture through the fine screen of a food mill set over a large bowl. Briefly mash the strawberries with a potato masher (to break them into pieces, not to obliterate them), and add them to the fruit purée. Stir in the sugar.
3. Pour half the mixture into the preserving pan. Boil the mixture over medium-high heat for about 5 minutes, until it mounds in a chilled bowl. Ladle the jam into pint or half-pint designated jam or Mason jars, and close the jars. Cook the rest of the fruit mixture in the same way, and fill more jars with the jam.
4. The jars can then be processed in a boiling-water bath: five minutes if the jars are sterilized first, 10 minutes if they’re not.