Reinforcement learning implies to associate an outcome with an action performed in the past, sometimes several seconds after its execution. How the artificial intelligence and brain associate these two events refers to the credit assignment problem (CAP). We hypothesized that the required temporal convergence of an eligibility trace encoding the planned action, and the referring outcome of that action takes place in the same brain area, to reinforce an optimal policy. By using a combination of pharmacogenetic/optogenetic manipulations and one-photon calcium imaging in awake behaving mice, we provide evidence that the premotor cortex can take over this role by emitting an eligibility trace, thereby solving the CAP. In a two-directional licking task with intra-session reversal learning (RevL), we first demonstrate that the premotor cortex maintains a directionality representation across the entire trial, including the post reward period. This post-outcome activity (POR) is refined following RevL and correlates with the behavioral performance. As the neuronal activity is not dependent on outcome but directionality, we conclude that the POR is compatible with the concept of an eligibility trace. Lastly, we found that optogenetic inhibition of the premotor cortex during the post-outcome and the preparation epoch impaired the RevL, suggesting a disconnection mechanism between the motor action and its value. In summary, we demonstrate that the premotor cortex can solve the CAP by maintaining the neuronal representation of an executed action, or eligibility trace, for several seconds in order to facilitate the temporal convergence of the planned action and its outcome.