Abstract: The fluid transfer device comprises a stator assembly incorporating a plurality of return channels which pick up the high speed fluid flow leaving a centrifugal impeller of one stage of the turbomachine for the purpose of rectifying, slowing down, and conveying said flow to the inlet of another centrifugal impeller of an adjacent stage of the turbomachine. Each return channel is constituted by a continuous shaped individual tubular element. A first continuous return channel is defined by a set of varying sections defined by parameters and extending normally to a mean line situated in a predefined plane (P1P2P3) containing the axis of the machine. The mean line has a rectilinear first portion, a curved second portion forming a circular arc of radius Rco2, and a rectilinear third portion. The various return channels are identical and can be derived one from another by rotation about the axis of the turbomachine.