The sheath (30) comprises a tube (31) and an end piece (32) that comprises a foot (33) introduced into an end portion of the tube (31), and a head (34) arranged in the extension of the tube (31). The foot (33) comprises, on the outer surface (40) thereof, a plurality of annular ribs (41-44) facing the inner surface (45) of the tube (31). The head (34) comprises a shoulder (38) facing the section (39) of the tube (31), projecting over the root of the foot (33). The end piece (32) and the tube (31) are attached to the periphery of at least one of said annular ribs exclusively by intrinsic welding. The method comprises the step of carrying out a peripheral tightening of the outer surface (37) of the tube on a level with the ribs (41 -44), and the step of applying a sonotrode to the outer surface (35-36) of the head (34).
