  The degree $d$ part of the cokernel $\mathsf C_d$ of the Johnson homomorphism
decomposes into irreducible $\mathrm{SP}$-modules indexed by partitions of
$d-2r$ for $r\geq 0$: $$\mathsf C_d\cong \mathsf C_d(d)\oplus \mathsf
C_d(d-2)\oplus\cdots.$$ In this addendum we calculate $\mathsf{C}_d(d)$
precisely: it is isomorphic to the $\mathrm{GL}(V)$-decomposition of a space of
coinvariants $(V^{\otimes d})_{D_{2d}}$, and the isomorphism is induced by
Enomoto and Satoh's trace map. This establishes Conjecture 7.2 of the paper
"The Johnson Cokernel and the Enomoto-Satoh invariant."
