Derived McKay correspondence for finite special-linear quotient resolutions

Let $V$ be a vector space, let $G\subset SL(V)$ be a finite subgroup, and let $X\to V/G$ be a crepant resolution. Write $D^b_G(V)$ for the bounded derived category of $G$-equivariant coherent sheaves on $V$, and $D^b_{\operatorname{Coh}}(X)$ for the bounded derived category of coherent sheaves on $X$. Derived McKay conjecture. Under these assumptions, there exists an equivalence

$$D^b_{\operatorname{Coh}}(X)\cong D^b_G(V).$$

This is presented as a generalization of the $K$-theoretic McKay correspondence and is attributed in the source to Ruan. The source gives no evidence that the derived equivalence is resolved in this stated generality.