I asked one of the nation's experts on transitioning to answer your question, Titi Branch from Miss Jessie's in Brooklyn. This is what she had to say:
It sounds like a very common scenario we see in the salon all the time. The
top layers of her hair represent thermal damage from the straightening iron.
These pieces will never curl up. You have to either cut them off all
depending on how short they are or set them to be curly; like a rod sert or
a double strand twist. You are exactly right in advising her that she should
not cut these pieces unless shes committed to wearing her hair curly all the
time. The double strand twist or rod set is a temporary styling method that
a: prevents further thermal damage from straight styling and b: allows you
to maintain all of your length while wearing your hair so that it looks
curly. At this point you have to just let time take over and be patient.
Allow the new hair to grow in at the root and don't do straight styling so
that you may prevent further thermal damage on newly natural hair. Hope that
Co-Chief Executive Officer
Miss Jessie's LLC