Finite presentability conjecture for finitely generated non-elementary subgroups of $\operatorname{PSL}(2,\mathbb{R})$

Let $H$ be a finitely generated subgroup of $\operatorname{PSL}(2,\mathbb{R})$ that is non-elementary, meaning it is not an elementary subgroup.

Finite presentability conjecture. Then $H$ is finitely presented.

The conjecture concerns finite presentability of finitely generated non-elementary subgroups of the group of orientation-preserving isometries of the hyperbolic plane. The source presents it as an open conjecture; no resolution is given in the provided text.