  Degenerating the quantum queer Schur superalgebra ${\mathcal{Q}_q(n,r; R)}$
to the case $q=1$, the queer Schur superalgebra ${\mathcal{Q}(n,r)}$ is
obtained. In this article, we reconstruct the universal enveloping algebra
${U({\mathfrak{q}_n})}$ of the queer Lie superalgebra ${\mathfrak{q}_n}$ via
${\mathcal{Q}(n,r)}$, and achieve another explanation of the Schur-Weyl-Sergeev
duality. Finally, we depict the Schur-Weyl-Sergeev duality over $\mathbb{Z}$.
