  Let A be a standard graded Artinian algebra over a field of characteristic
zero and let z be a linear form in A. We define the central simple modules for
each such pair (A, z). Assume that A is Gorenstein. Then we prove that A has
the strong Lefschetz property if and only if there exists a linear form z in A
such that all central simple modules of the pair (A,z) have the strong
Lefschetz property. In the course of proof we need to extend the definition of
the strong Lefschetz property to finite graded modules over graded Artinian
algebra, which previously was defined only for standard graded Artinian
algebras.
