Encoding classical information into a quantum system is one of the most fundamental questions of quantum information theory. Classic results in this area include the Holevo bound and the Holevo-Schumacher-Westmoreland theorem. The setting in the latter can be imagined as a black box which takes a single random variable encoding the information as input and outputs a quantum state. The theorem then states that under appropriate conditions, a decoder exists. In this work, we prove that decoders for different settings can be combined into one simultaneous decoder which handles the setting where the black box takes as input the overall joint random variable. This resolves a long-standing open problem in quantum network information theory and was made possible by Sen's recent quantum joint typicality lemma. We demonstrate the use of our results for the quantum relay channel, a possible communication model for quantum repeaters.