You must check the transmission and engine codes on both the donor (2001) and recipient (2000) vehicles. These codes are usually found on a sticker on the transmission itself and also in documentation for the car. Then compare them to ensure they are a perfect match. A seemingly minor difference could prevent installation.
Even with matching codes, it's advisable to consult a mechanic experienced with these models before attempting the swap. There might be other compatibility issues not readily apparent. A simple mismatch could lead to significant damage.