Moynier ya nuna sha'awar fahimtar ra'ayoyin Dunant don ƙirƙirar ƙungiyar kulawa ta son rai don taimakon wadanda suka ji rauni a yaƙi kuma ya buɗe tattaunawa game da littafin a taron Geneva Society for Public Welfare. Wannan ya haifar da ƙirƙirar "Kwamitin Biyar", kwamiti na Society wanda aka kafa don bincika yiwuwar ra'ayoyin Dunant. Ƙarin mambobi na Hukumar, tare da Moynier a matsayin shugaban, sune Louis Appia Dunant, likitoci da Théodore Maunoir da Janar Guillaume-Henri Dufour. Ba da daɗewa ba, membobin Kwamitin sun canza sunan zuwa "Kwamitin Taimako na Duniya ga Wanda Ya Ji rauni" kuma a cikin 1876 ya karɓi sunan yanzu, Dufour ya zama mataimakin shugaban Kwamitin Ƙungiyar Red Cross ta Duniya (ICRC) kuma ya zama mataimakin shugabanta na farko.
Moynier