Fukaya's coherent-sheaf construction from Floer cohomology

Assume the Strominger–Yau–Zaslow fibration conjecture holds, let $(X,W)$ be the relevant mirror-symmetry data, and let $(L,b)$ be a Lagrangian brane. For each point $p\in\hat X$, identify it with a pair $(L_{q(p)},b(p))$, where $L_{q(p)}$ is the fiber over $q(p)\in B$. Fukaya's coherent-sheaf construction conjecture. The coherent sheaf $\mathcal E(L,b)$ is obtained as a holomorphic bundle on $\hat X$ whose fiber at $p$ is identified with

$$HF((L_{q(p)},b(p)),(L,b)).$$

This proposes the mirror correspondence between a Lagrangian brane and a coherent sheaf via Floer cohomology. The source attributes it to Fukaya and gives no resolution.