It is known that graded cyclic modules over S=K[x,y] have the Weak
Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The
purpose of this note is to study which conditions on S-modules ensure the
WLP. We give an algorithm to test the WLP for graded modules with fixed Hilbert
function. In particular, we prove that indecomposable graded modules over S
with the Hilbert function (h0,h1) have the WLP