Federated Learning (FL) can be affected by data and device heterogeneities, caused by clients' different local data distributions and latencies in uploading model updates (i.e., staleness). Traditional schemes consider these heterogeneities as two separate and independent aspects, but this assumption is unrealistic in practical FL scenarios where these heterogeneities are intertwined. In these cases, traditional FL schemes are ineffective, and a better approach is to convert a stale model update into a unstale one. In this paper, we present a new FL framework that ensures the accuracy and computational efficiency of this conversion, hence effectively tackling the intertwined heterogeneities that may cause unlimited staleness in model updates. Our basic idea is to estimate the distributions of clients' local training data from their uploaded stale model updates, and use these estimations to compute unstale client model updates. In this way, our approach does not require any auxiliary dataset nor the clients' local models to be fully trained, and does not incur any additional computation or communication overhead at client devices. We compared our approach with the existing FL strategies on mainstream datasets and models, and showed that our approach can improve the trained model accuracy by up to 25% and reduce the number of required training epochs by up to 35%. Source codes can be found at: https://github.com/pittisl/FL-with-intertwined-heterogeneity.