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I'm fairly certain that the Book left the spells it had collected for Hayate's use, so she probably still has access to Nanoha's Starlight Breaker and Fate's Plasma Lancer Shifts. She just doesn't use them in favor of her own spells from a meta-level, as the show would want to show her using spells unique to her and not those already used by Nanoha and Fate. It is, after all, fairly easy to learn spells from someone else if you know how. Nanoha taught Teana the Starlight Breaker, and Nanoha herself took Teana's Crossfire Shoot with little difficulty.
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