Identification of the F-different with the different

Let $R$ be an $F$-finite normal local ring of characteristic $p>0$, let $X:=\operatorname{Spec} R$, and let $D+B$ be an effective $\mathbb{Q}$-divisor on $X$, where $D$ is a normal prime divisor with defining ideal $Q\subseteq R$ and $D$ is not contained in $\operatorname{Supp} B$. Let $B_{R/Q}$ be the effective $\mathbb{Q}$-divisor on $D=\operatorname{Spec}(R/Q)$ induced by the restriction of the Frobenius map associated to $(X,D+B)$. The different $B_D$ of $(X,D+B)$ on $D$ is the divisor defined by adjunction. The F-different identification. The divisors coincide:

$$B_{R/Q}=B_D.$$

This identifies the divisor obtained from Frobenius restriction with the classical different, linking $F$-singularity methods with adjunction. The source gives no resolution status for this claim.