My opinion - it depends on the goal of your friend & her mother. If there's any chance that the quilt might be valuable as an antique, I would have it appraised and evaluated for professional repair before doing anything. Repairs and restoration can devalue the quilt.
If the goal is to simply preserve the quilt for the family, I would consider fusing the blocks onto muslin, then reassemble them into a quilt.
You might want to consider consulting a quilt restoration/preservation specialist for the best advice.