Suppose that = (MM ) is a graded manifold and consider a direct subsheaf of Derundefined and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ Derundefined, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ Derundefined such that for some superfunction f on undefined then the superfunction F = f − J(φ)(X) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.