To imitate her writing style read as much of her writing as you can. Look for common turns of phrase or idioms that she uses, look for a pattern in first and last sentences of correspondence (problem statement, well wishing, summing up, etc), look at the number and length of paragraphs used, does she commonly use passive voice (starting the sentence with the object rather than the subject).
Someone copying my style for emails would see a common pattern of statement of problem - steps taken - request for action. Common phrase would be "as your schedule allows", "Let me know if there is anything I can do", and "Please advise". My emails will contain a lot of passive voice.