Full measure universality and strong meagerness conjecture

For $X\subseteq\mathbb{R}$, call $X$ strongly meager if $X+M\neq\mathbb{R}$ for every Lebesgue measure zero set $M\subseteq\mathbb{R}$. Full measure universality characterization conjecture. A subset of $\mathbb{R}$ is full measure universal if and only if it is a strongly meager subset of $\mathbb{R}$. This is the dual of the classification of topologically universal sets. The source says the conjecture is open even for perfect sets and discusses models in which its negation is consistent, while consistency of the conjecture itself is not known.