I believe that you should repair it so that it can be used (or not) and also so that it would last longer. Unrepaired, I would be afraid that it would continue to deteriorate. You want this special gift to last for years.
Yes, definitely make a label for the quilt telling its story. There is value in the story. Who knows this might find its way to a museum many years from now.
Such a delightful gift from a cherished friend! You are both blessed to know each other.
warm quilt hugs, sue in CA