Let $n\ge 2$, let $\Omega\subset \mathbb C^n$ be a bounded domain with $C^\infty$ strictly pseudoconvex boundary, and set $M:=\partial\Omega$. If $u\in C^\infty(M;\mathbb C)$ is a CR function on $M$, then there exists a function $F\in \mathcal O(\Omega)\cap C^\infty(\overline{\Omega};\mathbb C)$ such that
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\begin{align*}
F|_M=u.
\end{align*}
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If $\Omega$ is connected, then this extension is unique.