Interatomic Coulombic decay (ICD) from an Auger-final dicationic state is observed in the Ar dimer. A 2p inner-shell vacancy created by photoionization is replaced with 3s and 3p vacancies via intra-atomic Auger decay. The Auger-final dicationic state is subject to ICD in which one of the 3p electrons in the same Ar atom fills the 3s vacancy while one of the 3p electrons from the neighboring Ar atom is emitted as an ICD electron. This ICD process is unambiguously identified by electron-ion-ion coincidence spectroscopy in which the kinetic energy of the ICD electron and the kinetic energy release between Ar+ and Ar2+ are measured in coincidence.