Wash and core the plums and cut into medium or smaller pieces.
Mix with the preserving sugar and lemon juice and let the juice steep overnight.
The next day, puree the plums in whole or in part with a hand blender. Heat in a high saucepan, stirring constantly, and bring to a boil.
Roughly chop the walnuts. Caramelize 1 to 2 tablespoons of sugar in a pan, add the chopped walnuts and roast briefly (not too dark!). Deglaze with the plum water. Add the caramelized nuts and the cinnamon stick to the plums and cook for 4 to 5 minutes while stirring.
Make a jelly test: put a little hot jam on a plate and let it cool down. If this becomes firm, the jam is ready. If not, continue cooking briefly or add a little lemon juice.
Immediately pour the jam into twist-off jars rinsed with hot water and close tightly. Turn the glasses upside down for about 5 minutes, then turn them over and let them cool.