In the comments of this question:
What does it mean when the extension of scalars is free?,
it is mentioned that if $ \psi: R \rightarrow S $ is a faithfully flat ring homomorphism between commutative rings, with $R$ Noetherian and $M$ a finitely generated $R$ module then if the extension of scalars $M \otimes_R S$ is a free $S$-module of rank one, $M$ is a (finitely generated) projective $R$-module of rank one. Can anybody provide me with a reference for this fact? I have tried looking in Bourbaki's Commutative Algebra book and have searched on the Stacks project but I could not find it.
Thank you in advance for any help!