Let $(M_0,\omega_0)$ and $(M_1,\omega_1)$ be smooth finite-dimensional second-countable Hausdorff symplectic manifolds of the same dimension, and let $H_i\subset M_i$ be embedded hypersurfaces with inclusion maps $j_i:H_i\to M_i$ for $i\in\{0,1\}$. Suppose that $f:H_0\to H_1$ is a diffeomorphism and that $f^*(j_1^*\omega_1)=j_0^*\omega_0$. Then there exist open neighbourhoods $U_i\subset M_i$ of $H_i$ and a diffeomorphism $F:U_0\to U_1$ such that $F|_{H_0}=f$ and $F^*\omega_1=\omega_0$ on $U_0$.