vector spaces – Isomorphism between $V^* otimes V$ and End$V$

If $V$ is a vector space and End$V$ is the set of endomorphisms from $V$ to $V$.

Defining a map from $V^*otimes Vrightarrow$ End $V$ by sending some element say, $fotimes v in V^* otimes V$ to endomorphism whose value at $win V$ is $f(w)v$.

I am trying to show this map is an isomorphism between $V^* otimes V$ and End $V$. I am trying to verify it using dual basis.

If some hint can be provided, it will be a great help!