A device which moves a die between a retracted position, thereby releasing the die from the device, and an advanced position, thereby fixing the die to the device. The device includes an inner body comprising an inner body wall, and an inner body set of inclined faces. A body comprises a longitudinal groove. The longitudinal groove comprises an inner wall which contacts the inner body wall. An intermediate body comprises a first longitudinal side comprising a longitudinal side set of inclined faces, and a second longitudinal side arranged opposite thereto. The first longitudinal side cooperates with the inner wall. The second longitudinal side cooperates with a first side of the die. The longitudinal side set of inclined faces cooperates with the inner body set of inclined faces. A relative movement between the intermediate body and the inner body moves the die between the retracted position and the advanced position.