Evenness of non-inner almost inner derivations of quasireductive Lie superalgebras

Let $L=L_\mathbf{0}\oplus L_\mathbf{1}$ be a quasireductive Lie superalgebra, and let an almost inner derivation of $L$ be a derivation that is almost inner, while an inner derivation is one induced by an element of $L$. Evenness conjecture. If an almost inner derivation of $L$ is not inner, then it is even, כלומר it belongs to the even component of the derivation Lie superalgebra.

This asserts that quasireductivity excludes non-inner almost inner derivations of odd parity. The supplied text does not state whether the claim is proved or remains open.