A sufficient condition for strong $F$-regularity

Let $(R,\mathfrak{m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I⊊R$. We prove that if $R$ is $S_2$ and $H_{\mathfrak{m}}^{d-1}(R\mathrm{/}I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular ring. In particular, under these assumptions, $R$ is a Cohen-Macaulay normal domain.