S-adelic Mordell–Lang conjecture for hyperbolic affine curves in tori

Let $F$ be a global field, let $X_F$ be a hyperbolic affine curve contained in $\mathbf P^1_F$, and let $j:X_F\rightarrow T_F$ be a closed immersion into a torus $T_F$. For a finitely generated subgroup $G$ of $T_F(F)$, let $\overline{G}^{S}$ denote its topological closure in $T_F(\mathbb A_F^S)$. S-adelic Mordell–Lang conjecture. There is a finite subscheme $Z\subset X$ such that

$$X(\mathbb A_F^S)\cap\overline{G}^{S}\subseteq Z(\mathbb A_F^S).$$

This is an adelic analogue of the Mordell–Lang principle for tori, formulated in the spirit of a question of Stoll. The supplied text presents it as a conjecture and does not state that it has been resolved in this generality.