Put the zucchini and strawberries in a large pot and stir in the lemon zest and lemon juice. Bring the ingredients to a boil over medium heat. Lower the heat and continue to simmer, uncovered, until the zucchini is tender, about 10 minutes.

Stir in the pectin. Return to a boil and stir in the sugar and crystallized ginger. Bring to a steady boil (this can take 3–5 minutes) and boil hard for 1 minute, stirring constantly and scraping the bottom of the pot. Remove from the heat and skim off any foam. Stir for 5 minutes to prevent the zucchini from floating in the jam.

Ladle into clean, dry 1/2-pint jars. Cool to room temperature before adding lids.