I would go to a store that sells mattress foam and start there. Foam comes in a huge variety of firmness, and you can test it at the store. Here's some info on upholstery foam. In the past, I have gone to Diamond Foam and Fabric in Los Angeles to buy foam, but we also stocked a lot of foam at the furniture company where I worked for over 30 years. Occasionally I would get some scraps at work for small projects.

I personally would not use any kind of loose filling for a futon, although a lot of them are made with cotton stuffing. You can glue batting to the upholstery foam to make it more comfortable.

Stuffing an entire mattress sounds like a big task and the results might be less than ideal. I would just buy a replacement futon mattress to fit in the cover you are making.

You have set a huge task for yourself! Why does your friend not just buy a mattress taht suits her?

You will need a core of high density foam that will have to be covered with batting and a couple of layers of fabric.

You will have to find a source that sells it. You cant buy it at a fabric store.

Then it will need to be wrapped in layers of dacron batting, the batting will need to be covered with a good fabric. Ticking was what used to be used.

I have worked with this foam to make long cushions for window seats when I used to have a home dec business .

You would be better off just buying one from some business that has the facilities and the materials to do it right.

Just getting it situated into the casing is very difficult.

You may want to rethink this.

I wouldnt do it.

My window cushions were more narrow than is a mattress. How I used to get the finished foam in there was to wrap it in plastic film so that it would slide. Then, reach in and tear the plastic away and pull that out. Still was a lot of wrestling and heavy pulling and that was only after careful construction of the outer cover.

Your outer cover wil need some structure to it, too . You may need some heavy cording around the edges of the outer cover in order for it to keep its shape, as a mattress. My window seat cushions had piping, just as do most cushions. But window seats dont get the level of use that a mattress would.

If your friend has that much of a problem that she can say for sure is caused by her current mattress, she just needs to get a different bed altogether.

Rethink, is my advice. Tell her that she needs a real new mattress. That is what friend are for , right?