The device has an attaching part (PF) intended to be integrated to a wall (DP). The attaching part is provided on a rear face (FR) of an immobilization unit that comprises a blocking element (EB1) intended to be introduced into a corresponding opening (OV) of the wall. Another blocking element (EB2) of the immobilization unit is located after the former blocking element, and intended to be moved to a final position. A wall edge (BP2) is opposed to another wall edge (BP1) for blocking the immobilization unit in the opening and integrating the device with the wall.