The boundary-of-quotients conjecture for rank-one lattices

Let $\Gamma$ be a cocompact lattice in $Sp(1,n)$ or $F_4^{-20}$, and let $\Gamma'$ be a Gromov-hyperbolic quotient of $\Gamma$. Write $\partial\Gamma'$ and $\partial\Gamma$ for their Gromov boundaries. The boundary-of-quotients conjecture. If $\partial\Gamma'$ is a sphere, then the kernel of the quotient map is finite and $\partial\Gamma'=\partial\Gamma$. This is stronger than what is needed for the generalized low-dimensional action conjecture and remains open.