  The Alperin--McKay conjecture relates irreducible characters of a block of an
arbitrary finite group to those of its $p$-local subgroups. A refinement of
this conjecture was stated by the author in a previous paper. We prove that
this refinement holds for all blocks of symmetric groups. Along the way we
identify a "canonical" isometry between the principal block of $S_{pw}$ and
that of $S_p\wr S_w$. We also prove a general theorem on expressing virtual
characters of wreath products in terms of certain induced characters. Much of
the paper generalises character-theoretic results on blocks of symmetric groups
with abelian defect and related wreath products to the case of arbitrary
defect.
