Combine quince pulp, cranberries and water in a large pot, non-reactive pot. Bring to a bare simmer, turn the heat to low and cover. You do this because the quince pulp rapidly becomes quite splashy and it’s best for everyone to keep that kind of splatter contained.
This isn’t a product that needs a ton of cooking, because the quince has already been cooked for around three hours. Really, you’re just gently simmering until the cranberries pop.
When the cranberries have popped (some might need a bit of convincing with the back of a wooden spoon), add the sugar and lemon zest. Stir to combine. Add a bit more water if the sauce has gotten too stiff (quince in very high in pectin, so vigorous setting is a possibility). Taste and adjust the sugar if you feel so moved.
At this point, you could also give it a bit of spice with the addition of cinnamon, nutmeg, allspice, ginger or cloves (I would pick just one or two). However, I like the simple taste of the fruit, so I leave it as is.
Fill jars, wipe rims, apply lids and bands and process in a boiling water canner for 15 minutes. This recipe will make approximately four pints. However, if you make less and plan to eat it fairly soon, you can skip the canning step. Just store it in the fridge until you’re ready to eat.