Combine the pureed strawberries, sliced rhubarb and 1 cup sugar in a large, non-reactive pot over medium-high heat. Bring to a low boil and then reduce the heat to medium-low.
Stirring regularly, cook the fruit at a low simmer for 35 to 45 minutes, until it no longer looks watery and it sits up high in the bowl of a spoon. If the butter is making a splashy mess, use a splatter shield to control the mess.
When the butter has reduced to about half its original volume, taste it. If desired, add additional sugar (I rarely add it to mine, but I do like my preserves to be a little tart).
If any whole pieces of rhubarb remain, press them into the butter using the back of your spoon.
Once butter has finished cooking, remove the pan from the heat. Funnel butter into prepared half pint jars. Wipe rims, apply lids and rings, and process in a boiling water bath canner for 15 minutes (because this is a thick product, I like to process it longer than I do jams and jellies).
When time is up, remove jars from canner and place on a folded kitchen towel to cool.
Once jars are cool enough to handle, remove rings and test seals by grasping the edges of the lid and lifting the jar an inch or so off the countertop.
Any unsealed jars should be refrigerated and used promptly. Sealed jars should be stored in a cool, dark place and used within one year. For excellent & detailed step by step pictures/instructions go to simplebites.net.