What capability allows someone to change a page’s/post’s author?

The capability that controls setting the author would be edit_others_posts. Giving this capability to Authors would make it possible for them to edit other users posts/pages. You would need to be a bit more specific about what you are trying to accomplish for any further advice.

There aren’t any capabilities specific to just controlling the editing of the post/page author, but you could add your own capability to do such a thing.

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