Combine persimmon puree and sugar in a large heavy-bottomed pot.
Place the pot over low heat, dissolving the sugar. Increase to a high heat.
Bring the mix to a full rolling boil while stirring constantly until it thickens.
Add lemon juice and zest, and stir to incorporate fully.
Ladle hot jam into sterilized jars, and let cool completely to room temp if stored in the fridge. It does slightly thicken in the jars as it cools.