orthogonal factorization systems

I've placed a bet with a colleague that the following result appears in the literature. Please help me win. Claim: Suppose (E,M) is an orthogonal factorization system (unique lifts) on a symmetric monoidal category and X is a fixed monoid. If tensoring with X preserves maps in the class E, then (E,M) lifts to an orthogonal factorizaiton system on the category of X-modules. Regards, Emily Riehl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]