Conder–Džambić–Jones conjecture on alternating quotients of amalgamated free products

Let $A$ and $B$ be finite groups, and let $C$ be a subgroup of $A\cap B$ with index at least $2$ in $A$ and at least $3$ in $B$. The Conder–Džambić–Jones conjecture. All but finitely many alternating groups are homomorphic images of the amalgamated free product $A\ast_C B$. This conjecture concerns when finite alternating groups arise as quotients of amalgamated free products; it is presented as originating with Džambić and Jones and supported by Conder, and the supplied source gives no resolution.