Kit (11; 88; 98) which is intended to be implanted in a blood vessel, of the type comprising: - a tubular endoprosthesis which has an inner surface which delimits a channel having a longitudinal axis (X-X'); and - a prosthetic valve which is intended to be implanted in the channel, the valve comprising: • a carrier reinforcement which has an outer surface (35A, 35B; 35) which is intended to be pressed against the inner surface of the endoprosthesis, the reinforcement being able to be deformed radially from a folded position for placement to a deployed position for implantation; • a flexible shutter which is connected to the reinforcement and which can be deformed between a blocking position in which it is extended transversely and a release position in which it is contracted transversely under the action of the flow moving in the channel; characterised in that the inner surface has two portions (65, 67) having a variable cross-section along the longitudinal axis (X-X'), the portions (65, 67) forming a proximal stop and a distal stop, to block the axial displacement of the outer surface (35A, 35B; 35) along the inner surface in two opposing directions, the two portions (65, 67) being connected each other by a radially recessed support portion having a length substantially equal to the length of the outer surface (35A, 35B) of the reinforcement and delimiting, with the portions (65, 67) having a variable cross-section, a housing for receiving the reinforcement. - a tubular endoprosthesis which has an inner surface which delimits a channel having a longitudinal axis (X-X'); and - a prosthetic valve which is intended to be implanted in the channel, the valve comprising: • a carrier reinforcement which has an outer surface (35A, 35B; 35) which is intended to be pressed against the inner surface of the endoprosthesis, the reinforcement being able to be deformed radially from a folded position for placement to a deployed position for implantation; • a flexible shutter which is connected to the reinforcement and which can be deformed between a blocking position in which it is extended transversely and a release position in which it is contracted transversely under the action of the flow moving in the channel; characterised in that the inner surface has two portions (65, 67) having a variable cross-section along the longitudinal axis (X-X'), the portions (65, 67) forming a proximal stop and a distal stop, to block the axial displacement of the outer surface (35A, 35B; 35) along the inner surface in two opposing directions, the two portions (65, 67) being connected each other by a radially recessed support portion having a length substantially equal to the length of the outer surface (35A, 35B) of the reinforcement and delimiting, with the portions (65, 67) having a variable cross-section, a housing for receiving the reinforcement. • a carrier reinforcement which has an outer surface (35A, 35B; 35) which is intended to be pressed against the inner surface of the endoprosthesis, the reinforcement being able to be deformed radially from a folded position for placement to a deployed position for implantation; • a flexible shutter which is connected to the reinforcement and which can be deformed between a blocking position in which it is extended transversely and a release position in which it is contracted transversely under the action of the flow moving in the channel; characterised in that the inner surface has two portions (65, 67) having a variable cross-section along the longitudinal axis (X-X'), the portions (65, 67) forming a proximal stop and a distal stop, to block the axial displacement of the outer surface (35A, 35B; 35) along the inner surface in two opposing directions, the two portions (65, 67) being connected each other by a radially recessed support portion having a length substantially equal to the length of the outer surface (35A, 35B) of the reinforcement and delimiting, with the portions (65, 67) having a variable cross-section, a housing for receiving the reinforcement.