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Ensuring fairness of prediction-based decision making is based on statistical group fairness criteria. Which one of these criteria is the morally most appropriate one depends on the context, and its choice requires an ethical analysis. In this paper, we present a step-by-step procedure integrating three elements: (a) a framework for the moral assessment of what fairness means in a given context, based on the recently proposed general principle of "Fair equality of chances" (FEC) (b) a mapping of the assessment's results to established statistical group fairness criteria, and (c) a method for integrating the thus-defined fairness into optimal decision making. As a second contribution, we show new applications of the FEC principle and show that, with this extension, the FEC framework covers all types of group fairness criteria: independence, separation, and sufficiency. Third, we introduce an extended version of the FEC principle, which additionally allows accounting for morally irrelevant elements of the fairness assessment and links to well-known relaxations of the fairness criteria. This paper presents a framework to develop fair decision systems in a conceptually sound way, combining the moral and the computational elements of fair prediction-based decision-making in an integrated approach. Data and code to reproduce our results are available at https://github.com/joebaumann/fair-prediction-based-decision-making.