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A backup can now be opened straight from wherever it is kept. Share it from Files, iCloud Drive, Mail or Telegram, choose Reader, and it shows you what is inside — when it was made, how many books, how big — before asking whether to replace your library or merge into it. Nothing is restored until you answer.
Reader now tells the phone it is a reader for EPUB and FictionBook, rather than just one of the apps that can open them, so it should come up sooner when you open a book from somewhere else.