  Given a family of Laurent polynomials, we will construct a morphism between
its (proper) Gauss-Manin system and a direct sum of associated GKZ systems. The
kernel and cokernel of this morphism are very simple and consist of free
O-modules. The result above enables us to put a mixed Hodge module structure on
certain classes of GKZ systems and shows that they have quasi-unipotent
monodromy.
