That's a tricky one... if her story was already out there, I'd just recommend that you include a link to it in your author's notes and tell people to go read that one first. But if it's not yet published... you could write your bits, then set hers off by special quotes or something, but as a reader I think I'd find that jarring. Maybe it would work as flashbacks, but it sounds like you're trying to write the whole thing to *explain* the backstory, so that might not work very well.
Are you trying to write a self-sufficient story that uses whole scenes and paragraphs from her story? Or are you working within the elseworld universe she set up, maybe using some of *her* flashback sequences as present-day action in your story?
I think I'm leaning toward telling you to try to integrate her paragraphs/scenes with your story as non-jarringly as possible, and then add a detailed note at the *end* of the story, explaining which bits are hers. At the start, you could say something like, "thanks to my friend for letting me play in the universe she created; this is just a preview of what she's coming out with." Oh, and give her co-author credit, of course.
Have you talked to your friend about this?
It's hard for me to picture what you're talking about, but she'll have a much clearer understanding -- I hope!
PJ