Is the following true? What's a nice proof?

Let $M$ and $N$ be von Neumann algebras, and let $\phi:M\rightarrow N$ be a normal, surjective, *-homomorphism. Is there a normal *-homomorphism $\theta:N\rightarrow M$ with $\phi\circ\theta$ being the identity? If I cannot choose $\theta$ as a *-homomorphism, can I at least get a normal complete contraction?

This is, well, hinted at in the proof of Lemma 3.2 of http://pjm.math.berkeley.edu/pjm/2002/205-1/p09.xhtml but I don't follow the details (and they are proving it for weak* TROs: I think surely the von Neumann algebra case should be easier). Normal *-homomorphisms between von Neumann algebras have a very nice structure theorem, and maybe if I stared at that long enough I'd see an answer, but I thought I'd ask on MO...