Skycoach Conductor // All Aboard

Only the current controller of a prepared creature can cast the copy of its prepare spell in exile. It doesn't matter who owns that creature or who controlled it when it became prepared.

As an effect causes a creature with a prepare spell to become prepared (including effects that state that a creature "enters prepared"), that creature's controller creates a copy of that creature's prepare spell in exile. That copy remains in exile for as long as that permanent is on the battlefield and is prepared. That creature's controller may cast that copy as long as it remains in exile. As they cast it, that creature stops being prepared.

If a prepared creature stops being a creature, it will still be prepared, and the copy of its prepare spell will remain in exile. That permanent's controller will still be able to cast it. The same is true if a prepared creature becomes a copy of something else, even if it's then a permanent without a prepare spell.