I bought a new Mac Pro, but have lost my install discs for FCP Studio 3 upgrade from Studio 2, although I still have a copy of my serial number. A friend has offered to let me use his install discs for the full version of FCP Studio 3. Will the serial number I have work on this?

Don't see why this would not work. As the original CD's are all pressed from the same mould.

Yes it will work!