In medical imaging, accurately representing facial features is crucial for applications such as radiation-free medical visualizations and treatment simulations. We aim to predict skull shapes from 3D facial scans with high accuracy, prioritizing simplicity for seamless integration into automated pipelines. Our method trains an MLP network on PCA coefficients using data from registered skin- and skull-mesh pairs obtained from CBCT scans, which is then used to infer the skull shape for a given skin surface. By incorporating teeth positions as additional prior information extracted from intraoral scans, we further improve the accuracy of the model, outperforming previous work. We showcase a clinical application of our work, where the inferred skull information is used in an FEM model to compute the outcome of an orthodontic treatment.