Lehnert's universality conjecture for Thompson's group V

Let $V$ be R. Thompson's group, and call a group a $co\mathcal{CF}$ group if and only if it embeds as a finitely generated subgroup of $QAut(\mathscr{T}_{2,c})$. Lehnert's conjecture. Thompson's group $V$ is a universal $co\mathcal{CF}$ group. Lehnert's conjecture concerns the universality of $V$ among groups defined by this embedding property; the paper's surrounding discussion explains that $V$ embeds in $QAut(\mathscr{T}_{2,c})$ and that the two groups are bi-embeddable, but the supplied text does not establish the conjecture's resolution.