$R$ is a commutative ring with identity. $M^*={\rm Hom}_R(M,R)$ is the dual module of $M$. It is known that there is an $R$-homomorphism $M^*\otimes_R N\to {\rm Hom}_R(M,N)$.
My question is the following:
If $M$ is a projective $R$-module, $N$ is a finitely generated $R$-module, then it is an isomorphism?