Ouch! I would bring the quilt with me to fabric store and hope to match colors. Without knowing what the existing batting and fabric is, I would suggest appliquing directly on top of the existing fabric. Is there a pattern quilted on the background? What shape is the back in?
How much use/abuse is your friend expecting from this piece? If it is just a knockaround quilt, I'd make a new center section and machine applique. If it is now going to be treated as a treasured heirloom, handwork may be in order. I have had luck in the past slipping in fusible interfacing, fusing, and appliquing, but it is a whole lot of work, and that piece looks pretty beat up.
From the lack of fading where it is ripped, I would guess ut dates from no earlier than 1970s. This would be treated differently than one from the 1870s. Is the friend expecting it to come back in "like new" condition? That would be a huge undertaking.