How do I prove that $B(Y,\ell_2^n)^{**}$ is isometrically isomorphic to $B(Y^{**},\ell_2^n)$?

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How do I prove that $B(Y,\ell_2^n)^{**}$ is isometrically isomorphic to $B(Y^{**},\ell_2^n)$?

canonical embeddingof $J$ into $J^{**}$ is not surjective. $\endgroup$ – Yemon Choi Jul 24 '17 at 17:37