Jaeger et al.'s group-connectivity analogue of the 3-flow conjecture

For an abelian group $\Gamma$, a graph $G$ is $\Gamma$-connected if $(G,\beta)$ has a nowhere-zero flow for every $\Gamma$-boundary $\beta$. Jaeger et al.'s group-connectivity conjecture. Every $5$-edge-connected graph is $\mathbb{Z}_3$-connected.

This is a group-connectivity analogue of the 3-flow conjecture. The source reports that the conjecture is known for planar and projective-planar graphs, so the general case is resolved according to the supplied status evidence.