Jordan derivations of finitary incidence rings

Let $P$ be a preordered set, $R$ a ring and $FI(P,R)$ the finitary incidence ring of $P$ over $R$. We find a criterion for all Jordan derivations of $FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In particular, we prove that each Jordan derivation of the ring $RF{M}_I(R)$ of row-finite $I\times I$-matrices over $R$ is a derivation, if $\mathrm{\mid }I\mathrm{\mid }>1$.