The present invention relates to a process for the rapid synthesis of an AFX-structure zeolite comprising at least: i) mixing, in an aqueous medium, a FAU-structure zeolite having an SiO2 (FAU)/Al2O3 (FAU) molar ratio of between 2.00 and 100, a nitrogen-containing organic compound R, at least one source of at least one alkali and/or alkaline-earth metal M of valence n, with the following molar composition: (SiO2 (FAU))/(Al2O3 (FAU)) between 2.00 and 100, H2O/(SiO2 (FAU)) between 1 and 100, R/(SiO2 (FAU)) between 0.01 and 0.6, M2/nO/(SiO2(FAU)) between 0.005 and 0.45, wherein SiO2 (FAU) denotes the amount of SiO2 provided by the FAU zeolite and Al2O3(FAU) denotes the amount of Al2O3 provided by the FAU zeolite, until a homogeneous precursor gel is obtained; ii) hydrothermally treating said precursor gel obtained at the end of step i) under autogenous pressure at a temperature of between 120° C. and 250° C., for 4 to 12 hours.