Blockwise Z*-conjecture

Let $F$ be an algebraically closed field of characteristic $p>0$, let $G$ be a finite group, and let $B$ be a block of $FG$ with fusion system $\mathcal{F}=\mathcal{F}_D(B)$. Write $Z:=\mathrm{Z}(\mathcal{F})$ for the center of the fusion system, and let $b_Z$ denote the Brauer correspondent of $B$ in $\mathrm{C}_G(Z)$. Blockwise Z-conjecture.* The block $B$ is Morita equivalent to its Brauer correspondent $b_Z$ in $\mathrm{C}_G(Z)$. The conjecture is known for principal blocks; its general validity is left open in the source.