= Solution
<Charge conjugation> reverses the gauge charge, so
$$
\boxed{A_\mu\mapsto-A_\mu}.
$$
Using the antisymmetric spinor metric $\epsilon=i\sigma^2$, a compatible action on the two Weyl fields is
$$
\boxed{
\psi_L\mapsto i\sigma^2\psi_R^*,
\qquad
\psi_R\mapsto-i\sigma^2\psi_L^*}.
$$
Complex conjugation reverses the sign of $i$ and of the gauge representation, while $A_\mu\mapsto-A_\mu$ restores the original <gauge covariant derivative>. The identities $\sigma^2(\sigma^\mu)^*\sigma^2=\bar\sigma^\mu$ and $\sigma^2(\bar\sigma^\mu)^*\sigma^2=\sigma^\mu$ then exchange the two equations of motion. Unit phases can be inserted in the two spinor transformations without changing the conclusion, subject to the mass-term relation.
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