  We establish a relationship between two different generalizations of Lie
algebroid representations: representation up to homotopy and Vaintrob's Lie
algebroid modules. Specifically, we show that there is a noncanonical way to
obtain a representation up to homotopy from a given Lie algebroid module, and
that any two representations up to homotopy obtained in this way are equivalent
in a natural sense. We therefore obtain a one-to-one correspondence, up to
equivalence.
