= Solution
With the convention that the fields have charges $q_\Phi=2$ and $q_\Psi=1$, the <Noether current> may be written
$$
J^\mu
=2i\left(\Phi^*\partial^\mu\Phi-\Phi\partial^\mu\Phi^*\right)
+\overline\Psi\gamma^\mu\Psi,
$$
up to an overall sign convention for the generator. The field equations, including the invariant Yukawa interaction, give $\partial_\mu J^\mu=0$. Subject to vanishing flux at spatial infinity, the <Noether charge>
$$
Q=\int d^3x\,J^0
$$
is conserved and generates the global $U(1)$ transformations.
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