Let $M,N \subset \mathbb C^n$ be $C^2$ real hypersurfaces. Let $p \in M$, let $U,V \subset \mathbb C^n$ be open neighbourhoods of $p$ and $q:=F(p)$, and let $F:U\to V$ be a biholomorphism such that $F(U\cap M)=V\cap N$ after possibly shrinking $U$ and $V$. If $\sigma:V\to\mathbb R$ is a $C^2$ local defining function for $N$ near $q$, define $\rho:U\to\mathbb R$ by $\rho=\sigma\circ F$. Then $\rho$ is a $C^2$ local defining function for $M$ near $p$, and for every $Z,W\in T_{1,0,p}M$,

\begin{align*} \mathcal L_{\rho,p}(Z,W)=\mathcal L_{\sigma,q}(dF_pZ,dF_pW). \end{align*}