I googled 'jam jams'. The first site listed was the one that produced the pre-packaged jam jams. I googled "jam jams cookies'. Only recipes came up. I googled "jam jams history". Jam history sites came up. I googled "jam jams cookies history". Only recipes again. I wikipedia'd "jam jams". They don't have it on their site. Same with "jam jams cookies" and "jem jems". What they do have is a minor reference to "sandwich cookies", some of which have jam inside the 'cookie sandwich'.
Clearly there is a conundrum in the jam jams history area. How are we supposed to know where jam jams originated if the internet won't tell us? How are we supposed to find out how two ethnic/cultural groups that haven't talked to each other (except for maybe in the last 100 years) have the same cookie? How? Who else makes the jam jam? I guess we won't find out without some deep research. Here's the recipe.
Cream together: 1 cup margarine
1 cup brown sugar
6 tablespoon syrup
1 teaspoon vanilla
Add: 3 cups flour
2 teaspoon soda
1/4 teaspoon salt
Mix to a soft dough. Roll into balls and press down or roll dough and cut with cookie cutters. Bake at 350 degrees Fahrenheit. Spread jam between cookies when baked and press together.