Relation between H\'{e}non maps with biholomorphic escaping sets

Let $H$ and $F$ be two H\'{e}non maps with biholomorphically equivalent escaping sets, then there exist affine automorphisms $A_1$ and $A_2$ in $\mathbb{C}^2$ such that $$F=A_1\circ H \circ A_2$$ in $\mathbb{C}^2$.