The order conjecture for Morita-equivalent mapping torus categories

Let $\mathcal{A}$ be as in Theorem. Let $\phi$ and $\phi'$ be auto-equivalences satisfying the stated conditions, and let $M_\phi$ and $M_{\phi'}$ be their mapping torus categories. Assume that $M_\phi$ and $M_{\phi'}$ are Morita equivalent. Order conjecture. Then $\phi$ and $\phi'$ have the same order. This is proposed as a generalization of the theorem distinguishing mapping torus categories; the supplied text gives no resolution.