Nyorai kuenderera mberi kweiyi ndima - Mumwaka wa2011-12, Connacht yakakodzera mukombe wavo wekutanga weHeineken Cup. Pamberi pemwaka wekutanga weConnacht muchikamu chepamusoro cheEuropean rugby, timu yakasaina imwe scrum-hafu, Paul O'Donohoe anobva kuLeinster. Murphy akaramba ari Connacht's first choice pachinzvimbo ichi, achitamba mitambo makumi maviri mumutambo wa2011-12
, iyo yakanga yatumidzwazve kuti "Pro12". Mu Heineken Cup, zvisinei, Murphy akatanga maviri chete emitambo mitanhatu yechikwata, achiuya sechinotsiva mune mamwe maviri.