Homotopy conjecture for the Fukaya category completion functors

Let $\mathcal{N}(\bar{X},F_{0})$ be the Fukaya-type category and let $\widehat{\mathcal{W}}_{F}$ be its categorical formal completion. Suppose that $\widetilde{\Psi}:\mathcal{N}(\bar{X},F_{0})\to\widehat{\mathcal{W}}_{F}$ is the quasi-equivalence constructed as $\widetilde{\Psi}=\hat{\pi}^{*}\circ\Pi$, and let $\Psi$ be the Yoneda-type functor to the completion. Homotopy conjecture. The quasi-equivalence $\widetilde{\Psi}$ is homotopic to the functor $\Psi$. This would strengthen the preceding quasi-equivalence result by showing that the Yoneda-type functor $\Psi$ is itself a quasi-equivalence under the hypotheses of Theorem 2. Further analysis of the algebraic quasi-equivalence $\hat{\pi}^{*}$ is required to prove this.