The LNED conjecture for locally nilpotent derivations and E-derivations

Let $K$ be a field of characteristic zero, let $\mathcal{A}$ be a $K$-algebra, and let $\delta$ be a locally nilpotent derivation or E-derivation of $\mathcal{A}$. A $\vartheta$-ideal and a $\vartheta$-Mathieu-Zhao space are the corresponding notions used in the source. LNED conjecture. For every $\vartheta$-ideal $I$ of $\mathcal{A}$, the image $\delta(I)$ of $I$ under $\delta$ is a $\vartheta$-Mathieu-Zhao space of $\mathcal{A}$. This is the second conjecture posed by Wenhua Zhao in the supplied introduction; the text does not specify whether it has been resolved.