Morrison's movable cone conjecture for projective irreducible holomorphic symplectic manifolds

We prove a version of the conjecture in the title as a consequence of the Global Torelli Theorem for irreducible holomorphic symplectic manifolds $X$. Let $\mathrm{Bir}(X)$ be the group of birational automorphisms of $X$. As consequence it is shown that for each non-zero integer d there are only finitely many $\mathrm{Bir}(X)$-orbits of complete linear systems, which contain a reduced and irreducible divisor of Beauville-Bogomolov degree $d$. A variant hold for degree zero as well.