Equality of group and group-list edge chromatic numbers

Let $G$ be a simple graph. Denote its group edge chromatic number by $\chi'_g(G)$ and its group list edge chromatic number by $\chi'_{gl}(G)$. Equality conjecture. For every simple graph $G$,

$$\chi'_g(G)=\chi'_{gl}(G).$$

This is presented alongside the proposed analogue of Vizing's theorem as a conjecture about the coincidence of group edge choice parameters. The supplied status evidence marks the candidate as resolved, but gives no identifying theorem or reference.