Pit plums; do not peel. Grind or finely chop. Measure 5 cups into a 6- or 8- quart saucepot. Stir in walnuts, lemon peel and juice.
Prepare jars (wash, inspect rims, sterilize in boiling water or dishwasher). Keep lids hot until ready to fill jars.
Measure sugar into separate bowl. Stir fruit pectin into fruit in saucepot. Add butter. Bring mixture to full rolling boil on high heat, stirring constantly. Quickly stir in all sugar. Return to full rolling roil and boil exactly one minute, stirring constantly. Remove from heat. Gently stir in rum. Skim off any foam with a metal spoon. (I usually skip skimming, unless I’m processing for the county fair.)
Ladle quickly into prepared jars, filling to within 1/8 inch of tope. Wipe jar rims and threads. Cover with two piece lids. Screw bands tightly. Invert jars 5 minutes, then turn upright, or follow water bath method recommended by the USDA. After jars are cool, check seals.
Makes about 8 (1 cup) jars.