Center-realization conjecture for 2-Morita equivalent condensable algebras

Let $\CC$ be a modular tensor category, let $(A_1,A_2)$ be a 2-Morita-equivalent pair of condensable algebras, and let $\phi:\CC_{A_1}^{loc}\simeq\CC_{A_2}^{loc}$ be the associated equivalence. Construct $B_\phi$ by choosing an indecomposable summand as described in the source, and let $\operatorname{Ext}_{A_i}(B_\phi)$ denote its extension over $A_i$.

Center-realization conjecture. An indecomposable subalgebra

$$B\hookrightarrow\operatorname{Ext}_{A_1}(B_\phi)\ot\operatorname{Ext}_{A_2}(B_\phi)$$

is the 1d condensable algebra corresponding to $(A_1,A_2)$, in the sense that

$$Z_l(B)\cong A_1,\qquad Z_r(B)\cong A_2.$$

This would establish the converse direction needed to recover 1d condensable algebras from 2-Morita-equivalent pairs. The source gives no proof or resolution.