Aschenbrenner–Friedl–Wilton's virtual-retract conjecture for fully relatively quasiconvex subgroups

Let $M$ be a mixed manifold, and equip $\pi_1M$ with its natural relatively hyperbolic structure. A subgroup $H$ of $\pi_1M$ is fully relatively quasiconvex if it has the property specified by the source's definition. A virtual retract is a subgroup that is a retract of a finite-index subgroup containing it.

Aschenbrenner–Friedl–Wilton's conjecture. If $H$ is a fully relatively quasiconvex subgroup of $\pi_1M$, then $H$ is a virtual retract. In particular, $H$ is separable.

This conjecture concerns subgroup separability in the relatively hyperbolic structure naturally associated with mixed 3-manifold groups. The source attributes it to Aschenbrenner, Friedl, and Wilton and does not state that it has been resolved.