Machine Unlearning (MU) is an increasingly important topic in machine learning safety, aiming at removing the contribution of a given data point from a training procedure. Federated Unlearning (FU) consists in extending MU to unlearn a given client's contribution from a federated training routine. While several FU methods have been proposed, we currently lack a general approach providing formal unlearning guarantees to the FedAvg routine, while ensuring scalability and generalization beyond the convex assumption on the clients' loss functions. We aim at filling this gap by proposing SIFU (Sequential Informed Federated Unlearning), a new FU method applying to both convex and non-convex optimization regimes. SIFU naturally applies to FedAvg without additional computational cost for the clients and provides formal guarantees on the quality of the unlearning task. We provide a theoretical analysis of the unlearning properties of SIFU, and practically demonstrate its effectiveness as compared to a panel of unlearning methods from the state-of-the-art.