Hyperkaehler Embeddings II

In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the restriction of a holomorphic symplectic form is non-degenerate on $N$. In particular, $N$ is even-dimensional. In present paper, we prove that there exist a hyperkaehler metric on $M$, such that the embedding of $N$ to $M$ is hyperkaehler.