An example exists in this paper, p19-20. In fact they also construct a Hopfian group $H$ with finite (cyclic) normal subgroup $F$ and $H/F$ non-Hopfian.
user6976
An example exists in this paper, p19-20. In fact they also construct a Hopfian group $H$ with finite (cyclic) normal subgroup $F$ and $H/F$ non-Hopfian.