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Polarization transfer to a bound proton in polarized electron knock-out reactions, A(e→,e′p→), is a powerful tool to look for an in-medium modification of the bound proton. It requires comparison to calculations that consider the many-body effects accompanying the quasi-free process. We report here measured components Px′, Pz′, and their ratio Px′/Pz′, of polarization transfer to protons bound in Ca40, which is described well by the shell model and for which reliable calculations are available. While the calculations capture the essence of the data, our statistical precision allows us to observe deviations that cannot be explained by simple scaling, including by varying the proton electromagnetic form factor ratio GE/GM. We further explore the deviations of the ratio of the polarization transfer components from that of a free proton, (Px′/Pz′)A/(Px′/Pz′)H, and its dependence on the bound-proton virtuality.