Universal equivalence of symplectic groups

In this paper, we prove a criterion of universal equivalence of symplectic linear groups over fields: two symplectic linear groups $\mathrm{Sp}_{2n}(K)$ and $\mathrm{Sp}_{2m}(M)$, where $n,m\geq 1$ and $K$ and $M$ are infinite fields of characteristic not equal to $2$, are universally equivalent if and only if $n=m$ and the fields $K$ and $M$ are universally equivalent.