The invention relates to an adapter (14) for transferring a substance from a first container (10) into a second container, comprising a circumferential wall (47) suitable for housing the first container, along which a cannula body (64) extends and by which said cannula body is coaxially surrounded at least in part, said adapter also comprising a hollow cylindrical section (26), which is connected to the cannula body and can be connected to the second container. The cannula body extends with the longitudinal axis thereof perpendicular to one side of a wall (24) running transversely with respect to the circumferential wall and the hollow cylindrical section extends with the longitudinal axis thereof perpendicular to the other side of the wall. The adapter (14) has a cup-shaped outer body (18) having an outer circumferential wall (32) and the wall (24), which runs transversely with respect to the longitudinal axis of the outer body, which has an insert (46) having the circumferential wall (47) which houses the container.
