  We show that the fermionization of the Monster CFT with respect to
$\mathbb{Z}_{2A}$ is the tensor product of a free fermion and the Baby Monster
CFT. The chiral fermion parity of the free fermion implies that the Monster CFT
is self-dual under the $\mathbb{Z}_{2A}$ orbifold, i.e. it enjoys the
Kramers-Wannier duality. The Kramers-Wannier duality defect extends the Monster
group to a larger category of topological defect lines that contains an Ising
subcategory. We introduce the defect McKay-Thompson series defined as the
Monster partition function twisted by the duality defect, and find that the
coefficients can be decomposed into the dimensions of the (projective)
irreducible representations of the Baby Monster group. We further prove that
the defect McKay-Thompson series is invariant under the genus-zero congruence
subgroup $16D^0$ of $PSL(2,\mathbb{Z})$.
