Extension of 2-Morita equivalence to braided fusion categories

Let $\CC$ be a braided fusion category, and let $A,B$ be $E_2$-algebras in $\CC$. Define two $E_2$-algebras to be $E_2$-Morita equivalent when their module categories are $E_1$-Morita equivalent.

Braided 2-Morita conjecture. This definition of $E_2$-Morita equivalence extends to braided fusion categories without requiring non-degeneracy.

For modular tensor categories, the source relates $E_2$-Morita equivalence to equivalence of local module categories. The proposed extension removes the modular non-degeneracy assumption, but no proof or resolution is supplied.