  A.S. Dugas and R. Mart\'{i}nez-Villa proved in \cite[Corollary 5.1]{dm} that
if there exists a stable equivalence of Morita type between the $k$-algebras
$\Lambda$ and $\Gamma$, then it is possible to replace $\Lambda$ by a Morita
equivalent $k$-algebra $\Delta$ such that $\Gamma$ is a subring of $\Delta$ and
the induction and restriction functors induce inverse stable equivalences. In
this note we give an affirmative answer to a question of Alex Dugas about the
existence of a $\Gamma$-coring structure on $\Delta$. We do this by showing
that $\Delta$ is a Frobenius extension of $\Gamma$.
