The implant has a fusion module (6) arranged on a support module (1) and including holders for a transfacetal fastening unit. The support module includes a connecting link body (2), a slide (3) and jaw elements (4, 4'), which have contact surfaces (43) for a lamina on outer sides. The outer sides point away from each other. The jaw elements are longitudinally displaceably arranged on a guide so that a distance of the fusion module is changeable using the body and the slide. The fusion module includes a main bearing (60) at an upper facette and a counter bearing at a lower facette. Independent claims are also included for the following: (1) a set comprising a fusion implant and an instrument (2) a method for inserting a fusion implant.