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I don't see that there would be anything wrong with it as long as 1)they are familiar with the story world 2) they keep things as canon as possible and 3)it is acknowledged by the publisher that it is only based on the original author's work and not something that they were writing when they died. The last being optional if they are just tying up loose ends on a manuscript that the original author was almost done writing when they passed on of course.
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