Conjectural reverse inclusion for microlocal Arthur packets

In the setting of Theorem, let $G^{\Gamma}$ be an extended real reductive group, let $\psi$ be an Arthur parameter, and let the notation $\Pi^z(G^{\Gamma})^{mic}_{\psi}$ and $R^{\mathfrak g}_{\mathfrak q_1}R^{\mathfrak m_1}_{\mathfrak q_2}\Pi^{zz(\rho_{\mathfrak u_1})z(\rho_{\mathfrak u_2})}(M_2^{\Gamma})^{mic}_{\psi_2}$ be as in that theorem. Microlocal packet induction conjecture.

$$\Pi^z(G^{\Gamma})^{mic}_{\psi}=[R^{\mathfrak g}_{\mathfrak q_1}R^{\mathfrak m_1}_{\mathfrak q_2}\Pi^{zz(\rho_{\mathfrak u_1})z(\rho_{\mathfrak u_2})}(M_2^{\Gamma})^{mic}_{\psi_2}].$$

The source explains that the inclusion from left to right follows from the preceding theorem and conjectures the reverse inclusion; the equality is therefore presented as a conjectural refinement and remains open in the supplied text.