If $M = \partial W$, with $W$ parallelizable, then an embedding $\iota : M \to S^{n+k}$ extends to an embedding $W \to D^{n+k+1}$

Question

Suppose $M$ is an $n$-dimensional $s$-parallelizable manifold which is the boundary of the parallelizable compact manifold $W$. It is claimed in Milnor & Kervaire's Groups of Homotopy Spheres paper that an embedding $\iota : M \to S^{n + k}$ (for $k > n+1$) may be extended to an embedding $W \to D^{n+k+1}$. I can't see why this is true, and they don't give a reference. Can anyone see why this is true, or give a reference?