Yes. Once we get the moon to be stable above one point of the earth, there would be (nearly) no force on the rope, and we might get the effect of a Space Elevator.
But the difficulty would be to get the moon into a suitable position, so it could serve as a counterwight.
This would probably lead to a lot of changes on earth, e.g related to the tides. Or to Astrology. But I'd like to focus on the opportunities, e.g rope-climbing-competitions ;-)
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