The one-endedness conjecture for positively Ricci-curved manifolds

Let $(M,g)$ be a complete, noncompact manifold with finitely many ends, each end outside a compact set diffeomorphic to a spherical shell. Assume that $M$ has everywhere positive Ricci curvature and that its injectivity radius is bounded below. One-endedness conjecture. $M$ has only one end. The source leaves open whether these curvature and injectivity-radius assumptions force one-endedness.