Could a natural satellite in geosynchronous orbit be used as a counterweight to a space elevator?

Could a natural satellite in geosynchronous orbit be used as a counterweight for a space elevator? Does the counterweight need to be of approximately the same weight as the anchor? If so, I suppose that would be one hell of an anchor.

I'm envisioning an inhabited alien world on which the resident civilization decides to build a space elevator. Could they use the natural satellite as part in parcel of the project? Could it be the counterweight? Or, as one of the answerers indicated, could it be inserted as a point along the elevator itself.

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Could a natural satellite in geosynchronous orbit be used as a counterweight to a space elevator?

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