Prepare your canner, jars, and lids.
In a large, deep saucepan, combine apricots, red currants, lemon zest, and lemon juice. Bring to a boil over medium-high heat.
Gradually stir in the sugar, and stir constantly to dissolve the sugar. Continue boiling hard for about 15 minutes, stirring frequently.
Test for gel stage (see note below), and skim off any foam.
Ladle the hot jam into sterilized jars, leaving about 1/4-inch headspace. Wipe the rims of the jars clean and place the sterilized lids on top, securing them with bands until fingertip tight.
Process jars in a water bath canner for 10 minutes (15 minutes if above 6,000 feet).
Remove jars from the canner and let cool on a towel. Check the seals after 12-24 hours, label, and store in a cool, dark place.