  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.
