Prepared exam essay matches published example My son (3rd yr zoology in the UK) has an exam tomorrow, in which the task is to write an essay on the history of a(ny) branch of science. The idea is that the students can research and prepare their essay in advance and in the exam write it down from memory.

Now, my son has prepared his essay (on a subject obvious given his degree) only to find out less than 48h before the exam (tomorrow morning) that his topic is identical to that of an example essay published by the department online (but of which he was unaware) and which is quite similar to his. Obviously, if now writing his essay as intended, it will come across as plagiarised.

Q1: So what can he do?
Q2: What should the lecture do (a) if informed/asked by the student or (b) if not informed by the student, but finding the coincidence upon marking?
Q3: Can the marker simply assume plagiarism or do they have to prove it?
I assume from your question that he didn't only see the published essay but also read it. Then it will be nearly impossible to write his own essay, because he will always (even if unintentionally) adjust his work to not look like plagiarism. That will, of course, only strengthen the impression that he is plagiarizing.
Thus, I would take what he has up to now, the prepared essay that he wrote before finding the published one online, not change it in any way (even if the urge to avoid plagiarism might be strong) and talk to the one responsible about it right now; showing the current essay to try to prove his story.
What happens then depends on the regulations in that class. But there should be a possibility to rewrite the exam, e.g. for sick students or for students that failed the first try; maybe he can get in there with a new topic.
I would not try to get a new topic done today, that would only result in a really bad grade.