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By a well known theorem of K. Morita, any equivalence between full module categories over rings R and S, are given by a bimodule RPS, such that RP is a finitely generated projective generator in R-Mod and S= EndR (P). There are various papers which describe equivalences between certain subcategories of R-Mod and S-Mod in a similar way with suitable properties of RPs. Here we start from the other side: Given any bimodule RPS we ask for the subcategories which are equivalent to each other by the functor HomŔ (P,-). In R-Mod these are the P-static (= P-solvable) modules. In this context properties of s-Σ-quasi-projective, wE-quasi-projective and (self-) tilting modules RP are reconsidered as well as Mittag-Leffler properties of Ps. Moreover for any ring extension R→ A related properties of the A-module ARP are investigated.