Contravariant-form and Whittaker-vector isomorphism conjecture

Let $\eta$ be a character of the nilpotent subalgebra, let $U\in\mathcal{Z}_\mathfrak{g}$, and let $I_\eta(U)$ be the associated Whittaker-induced module. Denote by $\Psi_{I_\eta(U)}$ the vector space of contravariant forms on $I_\eta(U)$, and let $H_0^\eta(\bar{\mathfrak{n}},I_\eta(U))$ and $H^0_\eta(\mathfrak{n},(I_\eta(U))^*)$ denote the corresponding twisted coinvariants and Whittaker vectors. Contravariant-form isomorphism conjecture. There are linear isomorphisms

$$\Psi_{I_\eta(U)}\cong(H_0^\eta(\bar{\mathfrak{n}},I_\eta(U)))^*\cong H^0_\eta(\mathfrak{n},(I_\eta(U))^*).$$

This packages contravariant forms as linear functionals on twisted coinvariants and as Whittaker vectors in the dual module; the source presents the identifications as a statement, with no resolution information beyond its surrounding proposition and proof.