  The Cauchy integral formula in Clifford analysis allows us to associate a
holomorphic function $\tilde f:L_n\to \C$ on the Lie ball $L_n$ in $\C^n$ with
its monogenic counterpart $f:B_1(0)\to \C^{n+1}$ via the formula $\tilde f(z) =
\int_{S^n}G_\om(z)\bs n(\om)f(\om)\,d\mu(\om)$, $z\in L_n.$ The inverse map
$\tilde f\mapsto f$ is constructed here using the Cauchy-Hua formula for the
Lie ball following the work of M. Morimoto \cite{Mori2}.
