On Lie automorphisms of simple rings of characteristic 2

Let $R,R'$ be prime rings of characteristic 2 such that one of them is not GPI. Then any Lie isomorphism $\phi\colon\,R\to R'$ is of the form $\sigma+\tau$, where $\sigma$ is an isomorphism or an antiisomorphism of $R$ into the central closure of $R'$ and $\tau$ is an additive mapping of $R$ into the extended centroid of $R'$. Analogous result holds for Lie automorphisms of matrice ring $R=M_n(F)$, $n\geq3$, where $F$ is algebraic closure of field.