Varieties of representations of finite-dimensional algebras in prime algebras

We prove that the pairs $(A_1,\mathfrak{G}_1)$ and $(A_2,\mathfrak{G}_2)$ have the same identical relations if and only if for some field extension $K_1\supset K$ the pairs $(K_1\otimes_K A_1,K_1\otimes_K\mathfrak{G}_1)$ and $(K_1\otimes_K A_2,K_1\otimes_K\mathfrak{G}_2)$ are semilinear isomorphic. Here $\mathfrak{G}_1$, $\mathfrak{G}_2$ are some finite dimensional $K$-algebras of signature $\Omega'$ and $A_1$, $A_2$ are some central prime algebras of signature $\Omega$.