Semicrossed products of simple C*-algebras

Let $(\text{A},\alpha )$ and $(\text{B},\beta )$ be C*-dynamical systems and assume that $\text{A}$ is a separable simple C*-algebra and that $\alpha$ and $\beta$ are *-automorphisms. Then the semicrossed products $\text{A}{\times }_{\alpha }{\text{bbZ}}^{+}$ and $\text{B}{\times }_{\beta }{\text{bbZ}}^{+}$ are isometrically isomorphic if and only if the dynamical systems $(\text{A},\alpha )$ and $(\text{B},\beta )$ are outer conjugate.