Endomorphisms of semigroups of invertible nonnegative matrices over ordered associative rings

Let $R$ be a linearly ordered noncommutative ring with $1/2$ and $G_n(R)$ be the subsemigroup of the group $\mathrm{GL}_n(R)$ consisting of all matrices with nonnegative elements. Endomorphisms of this group are described in the papaer for $n \geqslant 3$.