A replaceable end-piece which can be connected to the dispensing end, which is provided with connection means of the vapor nozzle of a coffee machine for heating and frothing a given quantity of milk contained in a jug, into which the nozzle is introduced. A tubular sleeve is provided with two ends, the first end of which is open and is provided with reversible connection means corresponding to those of the dispensing end of the nozzle. The sleeve defines at the inner side thereof a recess which extends in accordance with a longitudinal axis. The second end of the sleeve is also open and includes a body inserted therein, the body being provided with a plurality of channels connecting the recess to the external environment of the end-piece facing the second end of the sleeve.