Yes, I just follow a raspberry jam recipe. Here's a basic one:
2 qts. raspberries, washed and drained
1/3 C. water
1 t. lemon juice
1 T. grated lemon peel
1 package pectin
6 C. sugar
Combine raspberries, water, lemon juice, lemon peel and pectin in a large pan. Bring to a rolling boil over high heat, stirring frequently. Add sugar, return to a boil. Boil hard 1 minute. Remove from heat and let set 5 minutes. Spoon off any foam that may be on top.
Ladle into sterilized jars and process in a water bath for 10 minutes.
I haven't made jam with mulberries, but I do other stuff (bake into sponge cakes, , make mulberry liqueur, make frozen popsicles, etc). I just wanted to say: use them up really quickly. More than a day in the fridge, and I find they always start going mouldy. It's because they bruise and bleed so easily, I think. I've had to throw away too many batches because I put off using them, so please don't make my mistake!
It's such a short season, so enjoy.