Vanishing of morphisms from good to exceptional Verma modules

Let a good Verma module mean a Verma module with a weight space decomposition, and let an exceptional Verma module be a module of the form $\mathbb{M}({\kappa_{\diamondsuit}},\kappa_1,[\iota;m],\zeta)$ for $m\in\mathbb{Z}$. Vanishing conjecture. Any morphism from a good Verma module to an exceptional Verma module is zero. This would complete the expected description of morphisms between good and exceptional Verma modules: the paper establishes the corresponding vanishing in the direction from exceptional to good, while this opposite direction remains open.