A condensation heat exchanger including at least one helically-coiled tube, inside which a fluid to be heated can circulate, a deflector, and a shell mounted inside which the tube, the shell having a gas-discharge sleeve having a bottom and a facade for feeding and/or producing a hot gas, inside the shell. The shell comprises a tubular metallic shroud closed at its two ends by a facade and a bottom, wherein the bottom is made of composite plastic, the rear edge of the shroud has a plurality of fastening tongues, the bottom has, at its periphery, a plurality of fastening slots arranged along at least part of its circumference, each fastening slot bordered longitudinally by a first longitudinal rib projecting outwardly, and wherein each fastening tongue is inserted into a fastening slot and folded twice around the first rib.