We consider a two-hop transmission setup in the context of Non-Terrestrial Networks (NTNs). Explicitly, a noisy source signal should be compressed at an on-ground relay node before getting forwarded over an error-prone and rate-limited channel to a satellite transponder. The impacts of this imperfect forwarding should be integrated into the compressor’s design formulation. In full harmony with the Information Bottleneck (IB) principle, we choose the Mutual Information (MI) as the fidelity criterion and devise a data-driven algorithm, the Deep ForwardAware Vector Information Bottleneck (Deep FAVIB), to tackle the design problem, when solely a finite sample set is available. To this end, first we derive a tractable objective function and, later on, utilize it to train the encoder and decoder Deep Neural Networks (DNNs) in the introduced learning architecture. Our approach here, that is based on (generative) latent variable models, extends the well-known concepts of Variational Auto-Encoders (VAEs) and Deep Variational Information Bottleneck (Deep VIB) from remote source coding to joint source-channel coding. To corroborate the effectiveness of our data-driven approach, we also present several numerical results over a typical transmission scenario for NTNs.