Now, when you're talking about green tomatoes, are you talking about underripe tomatoes, as in this
Italian recipe, or you talking about tomatillos, apparently commonly made into a
tomatillo and lime jam (though I've also seen one with jalapeno peppers online)?
We've been making rhubarb-and-ginger jam in our house, using a mixture of an old-fashioned ruby-red rhubarb we've had for yonks and what appears to be a Triffid, a 'peach-flavoured rhubarb' stool donated by an adventurous friend. We used jam sugar (which has added pectin). How to store it? We put it in the fridge, but it ended up being stored in our tummies too quickly to know if that was a feasible method of long-term storage.
Serious jam-makers may also preserve by 'canning' - in other words, using a
high-pressure cooker designed for heat-sealing the Kilner jars you use.