Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field

Let $k$ be an $F$-finite field containing an infinite perfect field of positive characteristic. Let $(X,\mathrm{\Delta })$ be a projective log canonical pair over $k$. In this note we show that, for a semi-ample divisor $D$ on $X$, there exists an effective $\mathbb{Q}$-divisor ${\mathrm{\Delta }}^{\mathrm{\prime }}{\sim }_{\mathbb{Q}}\mathrm{\Delta }+D$ such that $(X,{\mathrm{\Delta }}^{\mathrm{\prime }})$ is log canonical if there exists a log resolution of $(X,\mathrm{\Delta })$.