A geosycnchronous orbit is one with a period equal to the earth's rotational period, which, contrary to popular belief, is 23hr-56min-4.09sec., not 24 hours. Thus, the required altltude providing this period is ~22,238.64 miles, or ~35,787.875 kilometers. The orbital velocity of satellites in this orbit is ~10,088.25 feet per second or ~6,877 MPH. The point on the orbit where the circular velocity of the launching rocket reaches 10,088.25 fps, and shuts down, is the point where the separated satellite will remain.
The required Hohman Transfer velocity to transfer from the geostationary orbit to the lunar orbit, a mean distance of 239,000 miles away, is 13,544fps. The spacecraft will arrive at the lunar orbit with a velocity of 3340fps, taking ~136 hours to get there.
Sufficient propulsion capability will be needed to execute an orbital plane change of from ~18.5º to 28.5º.