Electrochemical batteries are ubiquitous devices in our society. When employed in mission-critical applications, the ability to precisely predict their end-of-discharge under highly variable operating conditions is of paramount importance in order to support operational decision-making and to fully exploit the entire battery's lifetime. While there are accurate predictive models of the processes underlying the charge and discharge phases, the modelling of ageing remains an open challenge. This lack of understanding often leads to inaccurate models or the need for time-consuming calibration procedures whenever the battery ages or its conditions change significantly. This represents a major obstacle to the real-world deployment of efficient and robust battery management systems. In this paper, we introduce Dynaformer, a novel deep learning architecture which is able to simultaneously infer the ageing state from a limited number of voltage/current samples and predict the full voltage discharge curve for real batteries with high precision. In the first step of our evaluation, we investigate the performance of the proposed framework on simulated data. In the second step, we demonstrate that a minimal amount of fine-tuning allows Dynaformer to bridge the simulation-to-real gap between simulations and real data collected from a set of batteries. The proposed methodology enables the utilization of battery-powered systems until the end of discharge in a controlled and predictable way, thereby significantly prolonging the operating cycles and reducing costs.