In a different large saucepan or pot, combine the water and sweetener of choice and bring it to a full rolling boil.
Once it has boiled, take it off of the heat and place plums into the hot syrup and fold them in. Combine plums with the syrup gently so you do not break up the whole fruit.
Return the pot to the heat for 1 more minute then turn the heat completely off leaving the pan on the heat source. Let your plum filled pot sit there covered for 20 minutes. This will give the entire plum mixture time to get completely warm without cooking it. After it has set, remove the lid and give it a gentle stir.
Using your jar lifter, pull out your hot jars from the boiling water canner pot and set on your towel covered surface.
Place a funnel in your first jar and using a slotted spoon, scoop out the warmed plums and fill your jars up to the threads of the jar. Once they are all filled, then start filling up the jars with the syrup from the pot leaving a 1/2 inch headspace.
Use a clean utensil, like a chopstick or a plastic spatula, to remove any trapped air bubbles by gently poking down the inside sidewall of the jar. Do not stir!
Now retrieve your lids from the warm water in the pot and cover jars with them. Screw bands onto the lids well. They do not need to be super tight, just enough for the lid to get a good seal.
Now with the jar lifter, lower each filled jar BACK into the original large pot of water. After all jars are placed, fill it with enough water to cover the tops of the jars by at least 1 inch.
Turn the heat under the pot to high until it reaches a full boil. At this point, put on the lid and set a timer for 10 minutes.
Once the time is up, turn off the heat and retrieve the jars with the jar lifter and place on your towel you used earlier.
Let them sit at room temperature for 24 hours to completely cool.
As they are coolng you will hear the lids pop as they suck down to the jar opening, this is a good thing!
Store the cooled, sealed jars in a cool, dark place. Don't forget to label each jar with the contents and the date of canning for easy identification. They are good up to 18 months from the date of canning.