  For a finite group $G$, let $\tilde{\mathbb{Z}}$ be the semilocalization of
$\mathbb{Z}$ at the prime divisors of $|G|$. If $G$ is a Frobenius group with
Frobenius kernel $K$, it is shown that each torsion unit in the group ring
$\tilde{\mathbb{Z}} G$ which maps to the identity under the natural ring
homomorphism $\tilde{\mathbb{Z}} G \rightarrow \tilde{\mathbb{Z}} G/K$ is
conjugate to an element of $G$ by a unit in $\tilde{\mathbb{Z}} G$.
