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It was shown in Dung-Smith [2] that, for a module M, every module in σ [M] is extending (CS module) if and only if every module in σ [M] is a direct sum of indecomposable modules of length 2 or, equivalently, every module in σ [M] is a direct sum of M-injective module and a semisimple module. Here we charcterize these modules by the fact that every module in σ [M] is lifting or, equivalently, decompose as a direct sum of a semisimple module and a projective module in σ [M]. They are also determined by the functor ring of σ [M] being a QF-2 ring with Jacobson radical square zero.