Process for the production of an injection-moulded element with a front side and a reverse side, where there is, arranged on the front side of the injection-moulded element, a film element flush with the surface of an in-mould-coating layer, where the film element has an edge and defines an inner edge region which extends from the edge over a predetermined distance d1 running at right angles to the edge in the direction of the film element, where d1 is ≥ 1% of the width of the film element and is smaller than half of the width of the film element and where the process comprises the following steps in this sequence: - provision of a mould which in the closed state defines, between a first mould half which replicates the front side of the injection-moulded element and a second mould half which replicates the reverse side of the injection-moulded element, a cavity configured in a manner complementary to the injection-moulded element, - placing of the film element into the first mould half, - closure of the mould, - injection of a plastified thermoplastic material into the cavity in order to configure an in-mould-coating layer, - allowing the plastics material to solidify, - opening of the mould and - removal of the injection-moulded element, characterized in that the thickness of the film element is ≥ 20 μm to ≤ 1000 μm, the film element covers only a partial region in the first mould half, and at least during one portion of the injection of the plastified thermoplastic material at least the inner edge region of the film element is heated by one or more temperature-control elements present in the first mould half at least to a temperature T of 20°C below the Vicat softening point (determined in accordance with DIN ISO 306:2014 method B at 120 K/h of heating time) of the material of the film element and locally restricted heating of the mould is achieved by means of dynamic temperature control at the film element/in-mould-coating material boundary, where regions of the film element that do not belong to the inner edge region are not heated to the temperature T. where the film element has an edge and defines an inner edge region which extends from the edge over a predetermined distance d1 running at right angles to the edge in the direction of the film element, where d1 is ≥ 1% of the width of the film element and is smaller than half of the width of the film element and where the process comprises the following steps in this sequence: - provision of a mould which in the closed state defines, between a first mould half which replicates the front side of the injection-moulded element and a second mould half which replicates the reverse side of the injection-moulded element, a cavity configured in a manner complementary to the injection-moulded element, - placing of the film element into the first mould half, - closure of the mould, - injection of a plastified thermoplastic material into the cavity in order to configure an in-mould-coating layer, - allowing the plastics material to solidify, - opening of the mould and - removal of the injection-moulded element, - provision of a mould which in the closed state defines, between a first mould half which replicates the front side of the injection-moulded element and a second mould half which replicates the reverse side of the injection-moulded element, a cavity configured in a manner complementary to the injection-moulded element, - placing of the film element into the first mould half, - closure of the mould, - injection of a plastified thermoplastic material into the cavity in order to configure an in-mould-coating layer, - allowing the plastics material to solidify, - opening of the mould and - removal of the injection-moulded element, characterized in that the thickness of the film element is ≥ 20 μm to ≤ 1000 μm, the film element covers only a partial region in the first mould half, and at least during one portion of the injection of the plastified thermoplastic material at least the inner edge region of the film element is heated by one or more temperature-control elements present in the first mould half at least to a temperature T of 20°C below the Vicat softening point (determined in accordance with DIN ISO 306:2014 method B at 120 K/h of heating time) of the material of the film element and locally restricted heating of the mould is achieved by means of dynamic temperature control at the film element/in-mould-coating material boundary, where regions of the film element that do not belong to the inner edge region are not heated to the temperature T.