Lang's divisible-subgroup conjecture for affine subsets of abelian varieties

Let $A$ be an abelian variety defined over $\mathbb{C}$, let $U$ be an open affine subset of $A$, and let $F\subset \mathbb{C}^n$ be a finitely generated subgroup. Let $\operatorname{Div}(F)$ denote the divisible subgroup of $\mathbb{C}^n$ associated to $F$. Lang's divisible-subgroup conjecture. The intersection

$$\operatorname{Div}(F)\cap U(\mathbb{C})$$

is finite. This extends the preceding finiteness expectation from finitely generated subgroups to their associated divisible subgroups; the authors state that proving such a result is beyond their reach, and the supplied passage gives no resolution.