Wiegold's conjecture on Nielsen equivalence of finite simple group generating tuples

Let $\mathbf{F}_{r}$ be the free group of rank $r$, let $G$ be a finite simple group, and define

$$\operatorname{Epi}(\mathbf{F}_{r},G)=\{\phi\in\operatorname{Hom}(\mathbf{F}_{r},G):\phi(\mathbf{F}_{r})=G\}.$$

Wiegold's conjecture. If $r\geq 3$, then $\operatorname{Aut}(\mathbf{F}_{r})$ acts transitively on $\operatorname{Epi}(\mathbf{F}_{r},G)$. This is equivalent to asking whether all generating $r$-tuples of a finite simple group are related by Nielsen transformations. The source describes this as a well-known open problem, even for simple $G$.