Cubulating hyperbolic free-by-cyclic groups: the general case

Let $\mathrm{\Phi }:F\to F$ be an automorphism of the finite-rank free group $F$. Suppose that $G=F{⋊}_{\mathrm{\Phi }}\mathbb{Z}$ is word-hyperbolic. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.