Fusion conjecture for one-dimensional condensable algebras

Let $\CC$ be a modular tensor category, let $A$ be a condensable algebra, and let $B_1,B_2$ be 1d condensable algebras defining bimodule walls over the local-module category $\CC_A^{loc}$.

Condensable-algebra fusion conjecture. Their relative tensor product satisfies

$${}_{B_1}(\CC_A)_{B_1}\boxtimes_{\CC_A^{loc}}{}_{B_2}(\CC_A)_{B_2}\simeq{}_{B_1\ot_A B_2}\CC_{B_1\ot_A B_2},$$

where the tensor over $A$ is induced from $\CC_A^{loc}$.

The source notes the special case $A=\one$ as a direct corollary and uses the claim to describe fusion of domain walls. No proof or resolution is supplied.