Cotorsion pair extensions

Assume that S is an almost excellent extension of R. Using functors Hom R (S,.) and .. R S, we establish some connections between classes of modules and , cotorsion pairs and . If is a T-extension or (and) H-extension of , we show that is a (resp., monomorphic, epimorphic, special) preenveloping class if and only if so is . If is a TH-extension of , we obtain that is complete (resp., of finite type, of cofinite type, hereditary, perfect, n-tilting) if and only if so is