Let us assume you can tether the elevator at one end to the space station and the other end to the earth the tether would have to be about 22,000 miles long as to do so the space station must be in a geosynchronous orbit. The space station is around 200 miles up so the station and the point of attachment on the earth would be traveling at different speeds.
Another point to consider if the elevator (read cable) is metallic it will be cutting through the earth’s magnetic field and generating an extremely high voltage that would have to be drained off to earth. That will cause some severe RFI on the space station.
Then again there is the elevator that just hangs from the space station and burns off due to friction between the cable and the atmosphere. If this could be accommodated, then the package to be lowered on the elevator would encounter that same friction and most likely burn up when it reached the end of the elevator. Lets’ assume this system works and the package does not burn up. The cable will be trailing the space station by several hundred miles and you would never know where the package was when it reached the end of the cable.
In the past satellites would release film canisters at about 200 or so miles up and they would be retrieved in flight by a specially equipped C-130. Why not go this route. All you would have to do is scale the system up.
