Algebraic structures for Eilenberg-Moore algebras

I'm looking for some pointer to literature where I can find the following (or a similar) Theorem: Let $(T,\eta,\mu)$ be a monad. Assume we have an algebraic structure such that every free algebra for that monad carries one of those algebraic structures and such that all morphisms of the form $Tf$ and all $\mu_C$ preserve it. Then all Eilenberg-Moore algebras carry such a structure and all morphisms between them preserve it. Thanks Andrea Schalk University of Cambridge Computer Lab Andrea.Schalk@cl.cam.ac.uk