A connector module (31, 71) has a base body (21) having a first contact (27) for electrically contacting an optoelectronic module (72) to be positioned into a depression (36) in the base body, a second contact (25) for electronically contacting a board, and a conductive trace (23) for electrically connecting the first (27) and second (25) contacts on a surface of the base body (21), and a molded part (33), the molded part (33) being cast onto the base body (21) across a first part of the surface, and the base body (21) and/or the molded part (33) defining a through-opening (13, 19, 37) for introducing a fiber (73). The base body (21) and the molded part (33) form two jaws for gripping the fiber (73).