A method is for fabricating a device for injecting a filler material in the fluid phase into a root canal space, the device including an adapter nozzle, an auto-mixer connected to the adapter nozzle, an intra-oral injection nozzle positioned at the upper end of the auto-mixer. The method includes using a shape memory material to make the injection nozzle so as to be bendable according to a desired orientation. The method also includes arranging on the exterior surface of the injection nozzle, circular ribs defining a groove, and moulding the upper end of the auto-mixer in this groove so that the injection nozzle is lodged in position in the upper end while retaining a degree of freedom in rotation around its axis of symmetry, or one or multiple circular ribs parallel to each other.