A step in the proof of holomorphic Frobenius theorem

Question

Let $M$ be a complex manifold and $I$ be the almost complex structure on $TM_{\mathbb{R}}$, and $E$ be a rank $k$ distribution stable under $I$. Let $\psi\colon U \to V$ be a submersion whose fibre are maximal integral manifold of $E$, or say $\ker \psi_{p,*}= E_p$. Then we have a almost complex structure on $V_{\psi(p)} \simeq T_pM/E_p$. The problem is, if $\psi(p) = \psi(p')$, how can we show that the induced complex structure are the same?