Equivalent NRH subgroup conjecture for Floyd boundaries

Let $G$ be a finitely generated group and let $\mathbb H$ be a collection of proper subgroups. A group $H$ is non-relatively hyperbolic (NRH) if it is not hyperbolic relative to any collection of proper subgroups. A group acts geometrically finitely on its Floyd boundary when its action on that boundary is a geometrically finite convergence action.

NRH subgroup conjecture. If $G$ is hyperbolic relative to a collection of NRH proper subgroups, then $G$ acts geometrically finitely on its Floyd boundary.

The source states that the converse follows from its structural corollary and proves that this conjecture is equivalent to the Olshanskii–Osin–Sapir conjecture above. Its status therefore remains tied to that open conjecture.