Minkowski summand conjecture from acyclic translates

Let $A$ and $B$ be convex bodies in $\mathbb{R}^n$. For every vector $t\in\mathbb R^n$, consider the translate $A+t$ and its difference from $B$. Minkowski summand conjecture. If $(A+t)\setminus B$ is either empty or acyclic for every $t\in\mathbb R^n$, then $A$ is a Minkowski summand of $B$, meaning that there is a convex body $C$ such that $B=A+C$. The conjecture asks whether the acyclicity hypothesis, previously proved under an openness assumption on $B$, remains sufficient when $B$ is a convex body; no resolution is supplied in the source.