Modules with finite Cousin cohomologies have uniform local cohomological annihilators

Let A be a Noetherian ring. It is shown that any finite A-module M of finite Krull dimension with finite Cousin complex cohomologies has a uniform local cohomological annihilator. The converse is also true for a finite module M satisfying (S2) which is over a local ring with Cohen–Macaulay formal fibers.