\ell-Galois special subvarieties are absolutely special

Let $S$ be the base of the family considered in the paper. An $\ell$-Galois special subvariety is a closed irreducible complex subvariety maximal among those having a fixed generic $\ell$-adic algebraic Galois group; an absolutely special subvariety is defined analogously using the generic absolute Mumford–Tate group. \ell-Galois-to-absolute-special conjecture. Any $\ell$-Galois special subvariety is absolutely special.

Together with the preceding conjecture, this would make special, absolutely special, and $\ell$-Galois special subvarieties equivalent. The source does not report a proof or disproof.