A shoulder prosthesis assembly includes a metaglenoid element (7) having a plate (13) with a central tubular bushing (14) and members for anchoring it in the glenoid cavity. The assembly also includes a glenoid sphere (9) that fits over the metaglenoid element which has an axial screw that is (35) screwed into the bushing. The glenoid sphere has a member to facilitate installation thereof on the metaglenoid element. The member may include a pin (46) adapted to slide in the tubular bushing (14) and in an axial channel of the screw, so that the glenoid sphere (9) can be screwed into place without any risk of damaging the thread of the screw or the tapping of the bushing.