The almost self-dual fundamental lemma

Assume the relevant unramified hermitian-space setup and let $K_0(\varpi)$, $K'$, $\mathfrak{k}'$, $K_1^{{{{{{{{\flat}}}}}}}}$, and $K_1$ be the compact subgroups and lattices defined in the source. Let $G'$, $S$, and $\mathfrak{s}$ denote the homogeneous, inhomogeneous, and Lie algebra sides, with corresponding unitary targets. Almost self-dual fundamental lemma. The following transfers hold: the homogeneous test function $(-1)^{n-1}\frac{q^n-1}{q-1}\mathbf{1}_{\mathrm{GL}_{n-1}(O_F)\times K_0(\varpi)}$ transfers to $(0,\mathbf{1}_{K_1^{{{{{{{{\flat}}}}}}}}\times K_1)}$; the inhomogeneous function $(-1)^{n-1}\mathbf{1}_{K'}$ transfers to $(0,\mathbf{1}_{K_1})$; and the Lie algebra function $(-1)^{n-1}\mathbf{1}_{\mathfrak{k}'}$ transfers to $(0,\mathbf{1}_{\mathfrak{k}_1})$. The source explains that the Lie algebra part is equivalent to the ordinary Lie algebra fundamental lemma and that the other parts follow when $q\geq n$.