Wash 2 pint jars (or a few half-pint jars) so that they are ready to go when your preserves are ready to be canned.
Add the apricots to the boiling water in a bowl along with 1/2 cup sherry and the rosemary sprigs. Let soak until the apricots are rehydrated, about 30 minutes. Strain the apricots, reserving 1/2 cup of the liquid. Add the apricots, reserved liquid and lemon zest to a large non-reactive pan. Stir in the pectin.
Bring the mixture to a boil and add the sugar, lemon juice, chopped rosemary and remaining 1/4 cup sherry. Boil until the sugar is dissolved and the jam is thick (you can check by spooning the jam onto the back of a wooden spoon; if you can run your finger through it without it spreading, it is good!) for 20 to 30 minutes.
Transfer the cooked jam to the jars. Let the jam cool to room temperature. Serve right away, or keep in the refrigerator for up to 2 weeks.
If you want a less chunky jam, chop the apricots ahead of time, or add the jam to a food processor.