Step 1 Wash and pit the apricots, reserving 5 stones. If the apricots are big, quarter them; if small, cut them in half. Don't peel, but trim away any really smutty spots. Combine the apricots and sugar in a nonreactive wide-bottomed pan. Crack the shells of the 5 pits, and remove the kernels. Peel and chop the kernels finely. Add the kernels and the lemon zest to the apricots and sugar; stir well. Leave to macerate (or soften and break down) for at least 30 minutes, even overnight. Begin cooking when the apricots have released their juices.
Step 2 Sterilize 5 (7-ounce) canning jars or 4 (8-ounce) jars.
Step 3Bring the pot of fruit to a boil over a high heat, stirring as needed to keep it from sticking. As a yellow froth forms over the top, skim it off. Reduce the heat if the mixture begins to stick, but take care not to lower the temperature too much, or this will extend the cooking time as much as 20 to 30 minutes (and cause too much water to evaporate and the fruit to lose its texture).
Step 4As the foaming subsides, continue to stir to avoid scorching and cook the mixture for 10 to 15 minutes, until it reaches 220 degrees on a candy thermometer. If you don't have a thermometer, put a plate in the freezer before you begin cooking. To check the consistency of the jam, put dabs of the hot jam on the chilled plate, so it will cool and set quickly. The jam is done when it is loosely set and spoonable on the chilled plate with whole chunks of fruit still visible.
Step 5Add the lemon juice to the jam, stir and immediately remove from heat. Pour into warm sterilized jars and seal according to the jar manufacturer's instructions. Constance Spry, the Fannie Farmer of Britain, says to seal the jars either when they're hot or room temperature. The jars are easier to handle at room temperature.