What exactly does this mean? Is it a woman who is identified by having a book with her? (if so, the typical English equivalent would be "the woman with the book"). Or is it a female character from a book? (If so, the English equivalent would be "the woman in the book" or maybe "the woman from the book"). Or is this just one of Duolingo's nonsensical translation exercises...? I understand that English does not use genitive case the same way that Greek does or use the same prepositions in the same contexts (which is true when comparing languages in general), but I am trying to understand this better...
Yes, I see what you mean. As you say, prepositions don't lend themselves easily translation. The Greek means: "The woman who was mentioned in the book." Perhaps, the Eng. should be "The woman in the book?" I'll add "in" it sounds better but please give us your view.
Both "in" and "of" work if you mean the woman mentioned in that particular book
the woman's book = το βιβλίο της γυναίκας
The woman in the book or
the book's woman = η γυναίκα του βιβλίου
i.e the owner is in genitive
The woman of the book, for instance, might refer to Susannah. The creators of DL modern Gk probably put this one in because it helps students think about how to say "the woman's book." It's a good move pedagogically. That the phrase is not particularly common is not the important point. It is both possible and helpful. It could refer to the main character in John Fowles' novel The French Lieutenant's Woman, etc