A fluorination process for obtaining fluorinated compounds including at least one fluorosulfonyl group. More particularly, a process for preparing a fluorinated compound of formula (II), including at least one step of reacting a compound of formula (I) with anhydrous hydrofluoric acid in at least one organic solvent, in which R1 is equal to R2 except in the specific case where R1═Cl, then R2═F, and when R1 is equal to R2, R1 and R2 represent an electron-withdrawing group which has a Hammett parameter σp of greater than 0, such as F, CF3, CHF2, CH2F, C2HF4, C2H2F3, C2H3F2, C2F5, C3F7, C3H2F5, C3H4F3, C3HF6, C4F9, C4H2F7, C4H4F5, C5F11, C3F5OCF3, C2F4OCF3, C2H2F2OCF3, CF2OCF3, C6F13, C7F15, C8F17 or C9F19, and M represents a hydrogen atom, an alkali metal, an alkaline-earth metal or a quaternary ammonium cation.