The cyclic module conjecture for finite Gorenstein injective dimension

Let $R$ be a local ring, and let $M$ be a nonzero cyclic $R$-module of finite G-injective dimension. Cyclic module conjecture. If such an $M$ exists, then $R$ is Gorenstein. This conjecture extends the corresponding result for nonzero cyclic modules of finite injective dimension; the cited context does not establish whether it is open or resolved.