Wash jars, lids, and rings. Keep jars hot in a pot of simmering water; place a small plate in the freezer for testing set.
Rinse and destem the black currants, then drain well.
Combine black currants and water in a wide, heavy pot. Bring to a simmer over medium heat and cook, stirring, until skins split and fruit softens, 5–8 minutes.
Add the granulated sugar and lemon juice. Stir over low heat until the sugar fully dissolves, 2–3 minutes.
Increase heat to high and boil rapidly, stirring frequently and skimming foam, until the jam reaches 220°F/105°C or passes the wrinkle test on the chilled plate, 8–12 minutes. (For the wrinkle test, drop a spoonful on the cold plate, chill 30 seconds, then push with a fingertip; the surface should wrinkle and hold a line.)
Remove from heat and let the jam rest 5 minutes to let fruit distribute evenly.
Working with one hot jar at a time, ladle jam into jars, leaving 0.25 inch headspace. Wipe rims clean, apply lids, and screw on rings fingertip-tight.
For shelf-stable storage, process the jars in a boiling-water bath for 10 minutes (start timing when water returns to a full boil; adjust time for altitude if needed). For refrigerator jam, skip processing.
Transfer jars to a towel-lined counter and cool 12–24 hours. Check seals; store sealed jars in a cool, dark place for up to 1 year. Refrigerate unsealed or opened jars and use within 3–4 weeks.