dimensional $C^*$-Hopf algebra on unital $C^*$-algebras and unital inclusions of unital $C^*$-algebras. In this paper, we shall discuss the relation between the strong Morita equivalence for twisted coactions of a finite dimensional $C^*$-Hopf algebra on unital $C^*$-algebras and the strong Morita equivalence for the unital inclusions of the unital $C^*$-algebras induced by the twisted coactions of the finite dimensional $C^*$-Hopf algebra on the unital $C^*$-algebras.

Let us explain the problem in detail. Let $A$ and $B$ be unital $C^*$-algebras. Let $H$ be a finite dimensional $C^*$-Hopf algebra and $H^0$ its dual $C^*$-Hopf algebra. Let $(\rho, u)$ and $(\sigma, v)$ be twisted coactions of $H^0$ on $A$ and $B$, respectively. Then we can obtain the unital inclusions of unital $C^*$-algebras $A\subset A\rtimes_{\rho, u}H$ and $B\subset B\rtimes_{\sigma, v}H$. In the same way as in [@KT4:morita Example], we can see that if $(\rho, u)$ and $(\sigma ,v)$ are strongly Morita equivalent, then the unital nclusions $A\subset A\rtimes_{\rho, u}H$ and $B\subset B\rtimes_{\sigma, v}H$ are strongly Morita equivalent. In this paper, we shall discuss the inverse implication. Our main theorem is as follows: We suppose that the unital inclusions $A\subset A\rtimes_{\rho, u}H$ and $B\subset B\rtimes_{\sigma, v}H$ are strongly Morita equivalent in the sense of [@KT4:morita 