While network coverage maps continue to expand, many devices located in remote areas remain unconnected to terrestrial communication infrastructures, preventing them from getting access to the associated data-driven services. In this paper, we propose a ground-to-satellite cooperative federated learning (FL) methodology to facilitate machine learning service management over remote regions. Our methodology orchestrates satellite constellations to provide the following key functions during FL: (i) processing data offloaded from ground devices, (ii) aggregating models within device clusters, and (iii) relaying models/data to other satellites via inter-satellite links (ISLs). Due to the limited coverage time of each satellite over a particular remote area, we facilitate satellite transmission of trained models and acquired data to neighboring satellites via ISL, so that the incoming satellite can continue conducting FL for the region. We theoretically analyze the convergence behavior of our algorithm, and develop a training latency minimizer which optimizes over satellite-specific network resources, including the amount of data to be offloaded from ground devices to satellites and satellites' computation speeds. Through experiments on three datasets, we show that our methodology can significantly speed up the convergence of FL compared with terrestrial-only and other satellite baseline approaches.