A note on CR mappings of positive codimension

We prove the following Artin type approximation theorem for smooth CR mappings: given $M\subset \mathbb{C}^N$ a connected real-analytic CR submanifold that is minimal at some point, $M^\prime\subset \mathbb{C}^{N^\prime}$ a real-analytic subset, and $H\colon M\to M^\prime$ a $\mathcal{C}^{\infty}$-smooth CR mapping, there exists a dense open subset $\mathcal{O}\subset M$ such that for any $q\in \mathcal{O}$ and any positive integer $k$ there exists a germ at $q$ of a real-analytic CR mapping $H^k\colon (M,q)\to M^\prime$ whose $k$-jet at $q$ agrees with that of $H$ up to order $k$.