The finite-group realization conjecture for block fusion systems

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 defect group $D$. The fusion system $\mathcal{F}_D(B)$ is the fusion system on $D$ associated with the block, and $D\in\operatorname{Syl}_p(H)$ means that $D$ is a Sylow $p$-subgroup of $H$. Finite-group realization conjecture. For every block $B$ of $G$ with defect group $D$, there exists a finite group $H$ such that $D\in\operatorname{Syl}_p(H)$ and $\mathcal{F}_D(B)=\mathcal{F}_D(H)$. This asks whether every block fusion system can be realized as the fusion system of a finite group having the defect group as a Sylow subgroup.