An LED illumination module has a light-emitting diode and a rotationally symmetrical, one-piece, light-transparent adapter lens centered on a lens axis. This lens has an axially rearwardly open blind hole defined by a radially inwardly directed frustoconical light-receiving side surface and an axially rearwardly directed convex light-receiving base surface. The diode is axially shiftable in the hole. An axially forwardly directed convex light-output surface is coaxially surrounded by an axially forwardly directed and forwardly flaring frustoconical light-output surface. A radially outwardly directed and radially inwardly reflective surface extends generally from a front edge of the axially forwardly directed frustoconical light-output surface to a rear edge of the radially inwardly directed frustoconical surface.