Graduate student with abysmal English writing skills, how to help
My wife, who was a writing coach for scientists, once had great success with a native speaker of Japanese whose written English was poor. She suggested he write the first few drafts in his native language, so that he could be sure he had the main ideas right. Then he translated his own work into English as best as he could, ready for revision.

Another possible strategy with a similar goal (getting the structure and basic ideas right first) might be for you to sketch a first rough draft, with the theorems in place and some of the expository scaffolding. Then the student could work on fleshing out the proofs and adding details - to be revised, of course.

(I wish I could check that second strategy out with my wife.)