  Due to a theorem by Orlov every exact fully faithful functor between the
bounded derived categories of coherent sheaves on smooth projective varieties
is of Fourier-Mukai type. We extend this result to the case of bounded derived
categories of twisted coherent sheaves and at the same time we weaken the
hypotheses on the functor. As an application we get a complete description of
the exact functors between the abelian categories of twisted coherent sheaves
on smooth projective varieties.
