Wei's abelianization conjecture for invariant algebraic D-modules

Let $G$ be a connected algebraic group, let $n$ be a rank, and let $q\colon G\twoheadrightarrow G/[G,G]$ be the quotient map. Write $\sim$ for the relation of $D$-module isomorphisms. Wei's conjecture. Pullback along $q$ induces an isomorphism

$$\frac{\{\text{Invariant $D$-modules of rank $n$ on }G/[G,G]\}}{\sim}=\frac{\{\text{Invariant $D$-modules of rank $n$ on }G\}}{\sim}.$$

The conjecture proposes that invariant algebraic $D$-modules on a connected algebraic group are classified, up to isomorphism, by those on its abelianization. It is presented as Wei's Conjecture 4.6; no resolution is supplied in the given text.