I'm stuck with the following problem:

In Petit's work "Faster Algorithms for Isogeny Problems using Torsion Point Images", p. 8, he says that we can deduce $\ker \psi_{N_2}$ knowing the action of $\psi = \psi_{N_1'}\circ\psi_{N_2}$ on $E[N_2],$ where $\psi_{N_1'}$ and $\psi_{N_2}$ are isogenies of degree respectively $N_1'$ and $N_2$ and $\psi = \psi_{N_1'}\circ\psi_{N_2}$ an endomorphism on the elliptic curve $E$.

Well, I don't understand this statement. I've tried writing $[N_2] = \psi_{N_2}\circ \hat{\psi}_{N_2}$ and then fiddling with the expressions, but to no avail.

I have a feeling this problem is easy, but I'm stuck and would appreciate any help/ideas.