Wash the persimmons, then remove the stem and peel them.
Quarter each persimmon and remove any seeds and blemishes if you see them. Then roughly chop the persimmons.
Place the persimmons and water in a large saucepan and cook it over medium heat, stirring frequently, for about 10 minutes.
Add the sugar, salt, and lemon juice to the saucepan, stirring until the sugar dissolves. Then increase the heat and cook until the mixture reaches a rolling boil.
Reduce the heat slightly, and cook for about 15 minutes, stirring frequently and skimming off any foam that forms if you wish. Remove the pot from the heat and if the fruit is still fairly intact, use a spoon to mash it up into more of a puree. Or, carefully puree the mixture using a stick blender inserted into the pot until it is very smooth (I use this method).
Now spoon a little of the fruit mixture onto the plate you placed in the freezer. Let it stand for 30 seconds, then run a spoon through the jam.. If it wrinkles, the jam is set. If it is still pretty liquidy, return the pot to the heat and cook for a few more minutes, then retest.
Store the jam in clean, sterilized jar s in the fridge for up to 2 weeks, or can it to keep your jam for up to 1 year.
Notes
Adjust the sugar. I don't love a super sweet jam, yet sugar does have an important function in creating a gelled jam. A typical ratio of fruit to sugar is 1:1, but I do try to adjust it depending on the sweetness of the fruit and how sweet I can stand it! You will find your own method of jam development as you gain experience. For the first time trying a new recipe, I always recommend making it as written before experimenting.
Stir constantly. Near the end of the cooking process, when the jam is thick, watch it and keep stirring so that it doesn't stick to the pan and burn.
Use a cold plate. The best way to know if the jam has set properly is to place a spoonful on a cold plate and watch for the "wrinkle" when you draw a spoon through it. Get in the habit of popping a plate into the freezer when you start prepping your jam so that it has enough time to chill.
Try a candy thermometer. Alternatively, a candy thermometer can be used to check the doneness of the jam. The ideal temperature of jam should be between 217° and 222° F (220° F may be the sweet spot!).
Puree or not to puree. This is up to you. I prefer a very smooth jam so I puree it using my immersion blender. For more texture, leave it as it or smush it up a bit with a spoon.
Add vanilla. For a slight flavor difference, try a little vanilla or vanilla bean paste added to the jam after you puree it.