Lifting elements modulo radical in a an integral algebra over local, henselian ring.

Question

$A$ is a local, strictly henselian ring with residue field $k$. $R$ is an $A$-algebra with unity and it's integral over $A$. $J$ is the radical of $R$. We are given that $R/J \cong M_d(k)$, which has elementary matrices $E_{i,j}$ satisfying $E_{i,j}E_{k,l} = \delta_{j,k}E_{i,l}$ and $\sum_{i=1}^{d}E_{i,i} = I$. The paper mentions that these elements can be lifted to $R$ so that the lifts satisfy these same equations. Proof is not given but it mentions that this works since $J$ is radical, $R$ is integral over $A$ and $A$ is henselian. I couldn't find a proof of this neither could I construct one myself as I don't have much experience with this type of lifting. I will appreciate help.