(i) disposes firstly a hollow protective textile sleeve 1010 having an outer rest diameter D1 and an interior volume 1005 configured to receive one or several elongates element(s), and comprising a substantially annular front part 1015 having an open front end, on at least one expansion device (not represented), causing the expansion of at least the substantially annular front part 1015 of the protective sleeve 1010 along an outer perimeter D1′ substantially equal to D2. (ii) provides a hollow connecting textile sleeve 1035 having a main rest diameter D2, D2 being greater than D1, and a substantially annular rear part 1030 having a rear open end. The rear part 1030 of the connecting sleeve 1035 is brought into contact with the front part 1015 of the protective sleeve 1010 so that the front part 1015 of the protective sleeve 1010 is folded towards the outside and around the inner portion 1025 of the rear part 1030 of the connecting sleeve 1035. Then, (iii) forms the first electrically conductive, in particular at least partially annular, securing area 1020 in which the rear part 1030 of the connecting sleeve 1035 and the front part 1015 of the protective sleeve 1010 are at least partly secured. The protective sleeve 1010 comprises a protective textile body 1008 projecting from its annular front part 1015, and the connecting sleeve 1035 comprises a connecting textile body 1032 projecting from its annular rear part 1030 as represented in FIG. 12. During step ii), the rear part 1032 of the connecting sleeve 1035 is at least partially superimposed on the front part 1015 of the protective sleeve 1010 on at least the expansion device, the front part 1015 of the protective sleeve 1010 being disposed between said at least expansion device, and the rear part 1030 of the connecting sleeve 1035. The protective sleeve 1010 comprises a protective textile body 1008 projecting from its annular front part 1015, and the connecting sleeve 1035 comprises a textile connection body 1032 projecting from its annular rear part 1035. During step iii), said protective 1008 and connecting 1032 textile bodies are at least partly superimposed. The method then comprises the turning over (iv) of the body 1032 of the connecting sleeve 1035 so that the connecting sleeve 1035 and the protective sleeve 1010 are superimposed, especially only, according to the rear part 1030 of the connecting sleeve 1030 and the front part 1015 of the protective sleeve 1010.