On the Matlis duals of local cohomology modules

Let (R, m) be a commutative Noetherian local ring with non-zero identity, a an ideal of R and M a finitely generated R-module with aM not equal M. Let D(-) := Hom(R)(-, E) be the Matlis dual functor, where E := E(R/m) is the injective hull of the residue field R/m. We show that, for a positive integer n, if there exists a regular sequence x(1),...,x(n) is an element of a and the i-th local cohomology module H-a(i)( M) of M with respect to a is zero for all i with i > n then H-a(n) (D(H-a(n)( M))) = E.