Simplicity of the neutral-element stabilizer in a simple Moufang loop

Let $L$ be a nonassociative simple Moufang loop and let $H=\operatorname{Mlt}(L)_e$ be the stabilizer of the neutral element in the multiplication group of $L$. Simplicity conjecture. The group $H$ is simple. This concerns the structure of multiplication groups of nonassociative simple Moufang loops; the source does not state whether the conjecture has been resolved.