The virtual adjoint-cohomology conjecture for hyperbolic lattices

Let $\Gamma\subset\operatorname{Isom}(\mathbb H^n)$ be a lattice, let $\Gamma'\subset\Gamma$ be a finite-index subgroup, and let $\rho$ denote the relevant natural representation. Virtual adjoint-cohomology conjecture. There exists a finite-index subgroup $\Gamma'\subset\Gamma$ such that

$$H^1(\Gamma',\operatorname{Ad}(\rho))\ne 0.$$

The source presents this as a stronger cohomological expectation related to deformations and does not state a resolution.