In Part I of this series of papers, we made Riley's definition of Heckoid groups for $2$-bridge links explicit, and gave a systematic construction of epimorphisms from $2$-bridge link groups onto Heckoid groups, generalizing Riley's construction. In this paper, we give a complete characterization of upper-meridian-pair-preserving epimorphisms from $2$-bridge link groups onto even Heckoid groups, by proving that they are exactly the epimorphisms obtained by the systematic construction.
"Epimorphisms from 2-bridge link groups onto Heckoid groups (II)." Hiroshima Math. J. 43 (2) 265 - 284, July 2013. https://doi.org/10.32917/hmj/1372180515