low convergence in $ L ^ 2 $ and integral convergence involving test functions

Let $ Omega $ to be a bounded set of $ mathbb {R} ^ n $ and $ (f_n) _n subset L ^ 2 ( Omega) $ such as $ f_n to f in L ^ 2 ( Omega) $ weakly $ L ^ 2 ( Omega) $. Then for a given test function $ phi in C ^ infty_c ( Omega) $, do we have the following convergent property:
$$
int_ Omega | u_n | phi , dx to int_ Omega | u | phi , dx, quad textrm {as $ n to infty $.}
$$