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We provide a simple proof of strong duality for the linear persuasion problem. The duality is established in Dworczak and Martini (2019), under slightly stronger assumptions, using techniques from the literature on optimization with stochastic dominance constraints and several approximation arguments. We provide a short, alternative proof that is based on a direct argument to show the existence of optimal price functions, and on switching the roles of the primal and the dual to show that there is no duality gap.