Affine Weyl group conjecture for Harish-Chandra bimodules between quantizations

Let $Y$ be a conical symplectic singularity, let $\lambda,\lambda'\in\mathfrak{h}_Y^*$, and let $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda'},\mathcal{A}_{\lambda})$ denote the quotient of the category of Harish-Chandra $\mathcal{A}_{\lambda'}$-$\mathcal{A}_{\lambda}$-bimodules by the full subcategory of bimodules with proper associated varieties. Assume $\mathfrak{h}_0^*=\\{0\\}$. Let $\Lambda_Y\subset\mathfrak{h}_Y^*$ be the weight lattice and $W_Y^{ae}=W_Y\ltimes\Lambda_Y$ the extended affine Weyl group. Affine Weyl group conjecture. The category $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda'},\mathcal{A}_{\lambda})$ is nonzero if and only if $\lambda'\in W_Y^{ae}\lambda$. If $\lambda'\in W_Y^{ae}\lambda$, the categories $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda'},\mathcal{A}_{\lambda})$ and $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda},\mathcal{A}_{\lambda'})$ contain mutually inverse objects. In particular, there is an equivalence of right $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda})$-module categories

$$\overline{\operatorname{HC}}(\mathcal{A}_{\lambda'},\mathcal{A}_{\lambda})\cong\overline{\operatorname{HC}}(\mathcal{A}_{\lambda}).$$

This proposed description characterizes when Harish-Chandra bimodules between two quantizations exist and when they implement an equivalence; the source provides no evidence that the statement has been proved or refuted.