Uniqueness conjecture for the tensor-product isomorphism of quiver-variety homology modules

Let $\mathfrak g$ be the Lie algebra used in the quiver-variety construction, let $\mathbf w^1$ and $\mathbf w^2$ be the two framing data, let $\mathfrak L(\mathbf w^i)$ be the corresponding Lagrangian quiver varieties, and let $\widetilde{\mathfrak Z}$ be the relevant convolution space. Write $H_{\operatorname{top}}(-,\mathbb Q)$ for top homology, and let $[0]_{\mathbf w^1}$ be the distinguished vector. Tensor-product isomorphism conjecture. There exists a unique $\mathfrak g$-module isomorphism

$$H_{\operatorname{top}}(\mathfrak L(\mathbf w^1),\mathbb Q)\otimes H_{\operatorname{top}}(\mathfrak L(\mathbf w^2),\mathbb Q)\longrightarrow H_{\operatorname{top}}(\widetilde{\mathfrak Z},\mathbb Q)$$

whose restriction to $[0]_{\mathbf w^1}\otimes H_{\operatorname{top}}(\mathfrak L(\mathbf w^2),\mathbb Q)$ is the Thom isomorphism, followed by the inclusion $H_{\operatorname{top}}(\widetilde{\mathfrak Z}_1,\mathbb Q)\to H_{\operatorname{top}}(\widetilde{\mathfrak Z},\mathbb Q)$. The statement is presented as a conjecture in the source; no resolution evidence is supplied in the given text.