Process for the transfer of at least a portion of a composite film onto a flexible polymer membrane, the composite film comprising a matrix made of thermoplastic polymer inside which are dispersed particles conferring physical properties on this composite film, the exodiameter of the particles being between 1 nm and 100 μm and the volume of the particles inside the composite film representing more than 1% of the volume of this composite film, this process comprising: α) the deposition of the composite film directly on a rigid substrate made of a material other than a polymer and having a thickness strictly greater than the thickness of the composite film, the composite film then exhibiting an external face turned the opposite way from the rigid substrate, then β) the transfer of at least a portion of the composite film deposited on the rigid substrate to the membrane by stamping, characterized in that, during stage β), the flexible membrane is used as a buffer and comprises, for this, the following operations: 1) the movement of the membrane both: - into an assembled position in which a central portion of the membrane closes up, in a way leaktight to a fluid, an opening of a reservoir, this central section then exhibiting a rear face directly exposed to the inside of the reservoir and a front face on the opposite side, and - into an active position in which a first zone of the front face is directly in contact on the external face of the composite film, 2) the heating of the composite film in order for its temperature to exceed the glass transition temperature of its matrix, so as to soften it, 3) when the composite film is softened and when the membrane is both in its assembled position and in its active position, the fluid inside the reservoir uniformly compresses the first zone against the external face of the composite film in order to adhesively bond this first zone to this external face with an adhesive force greater than the adhesive force which holds the composite film on its rigid substrate, then 4) the movement of the membrane from its active position to a retracted position in which its front face is further from the rigid substrate than in its active position, this movement of the membrane from its active position to its retracted position separating, from the rigid substrate, the portion of the composite film adhesively bonded to the first zone. α) the deposition of the composite film directly on a rigid substrate made of a material other than a polymer and having a thickness strictly greater than the thickness of the composite film, the composite film then exhibiting an external face turned the opposite way from the rigid substrate, then β) the transfer of at least a portion of the composite film deposited on the rigid substrate to the membrane by stamping, 1) the movement of the membrane both: - into an assembled position in which a central portion of the membrane closes up, in a way leaktight to a fluid, an opening of a reservoir, this central section then exhibiting a rear face directly exposed to the inside of the reservoir and a front face on the opposite side, and - into an active position in which a first zone of the front face is directly in contact on the external face of the composite film, - into an assembled position in which a central portion of the membrane closes up, in a way leaktight to a fluid, an opening of a reservoir, this central section then exhibiting a rear face directly exposed to the inside of the reservoir and a front face on the opposite side, and - into an active position in which a first zone of the front face is directly in contact on the external face of the composite film, 2) the heating of the composite film in order for its temperature to exceed the glass transition temperature of its matrix, so as to soften it, 3) when the composite film is softened and when the membrane is both in its assembled position and in its active position, the fluid inside the reservoir uniformly compresses the first zone against the external face of the composite film in order to adhesively bond this first zone to this external face with an adhesive force greater than the adhesive force which holds the composite film on its rigid substrate, then 4) the movement of the membrane from its active position to a retracted position in which its front face is further from the rigid substrate than in its active position, this movement of the membrane from its active position to its retracted position separating, from the rigid substrate, the portion of the composite film adhesively bonded to the first zone.