Free-factor formulation of Wiegold's conjecture

Let $F_n$ be the free group of rank $n$, let $G$ be a finite simple group, and let

$$\Psi:F_n\twoheadrightarrow G$$

be an epimorphism. A proper free factor is a free factor $H<F_n$ with $H\neq F_n$.

Wiegold's free-factor conjecture. If $n\geq 3$, then $F_n$ has a proper free factor $H$ such that $\Psi(H)=G$.

The paper presents this as an equivalent reformulation of Wiegold's connectivity conjecture, useful for generalization to infinite groups. Its general validity remains open.