Uniqueness of fmap in monads

Question

Given a monad with return and >>=, apparently fmap f m = m >>= return . f is a valid definition that respects both the functor and monad laws.

But is this definition unique? I mean, if there is another fmap' that respects both laws, does it follow that fmap' = fmap?

Can fmap f m = m >>= return . f be derived solely from the functor and monad laws?