Zero-sum partition conjecture for finite Abelian groups with multiple involutions

Let $\Gamma$ be a finite Abelian group of order $n$ with more than one involution. Let

$$n-1=r_1+r_2+\cdots+r_t$$

be a partition of $n-1$ with $r_i\geq 3$ for $1\leq i\leq t$, where $t$ is any positive integer. Zero-sum partition conjecture. There is a partition of $\Gamma\setminus\{0\}$ into pairwise disjoint subsets $A_1,A_2,\ldots,A_t$ such that

$$|A_i|=r_i\quad\text{and}\quad \sum_{a\in A_i}a=0$$

for $1\leq i\leq t$. The conjecture is true for groups isomorphic to $(\mathbb{Z}_2)^m$, as proved by Egawa; the parser marks this candidate as resolved, although the supplied context does not state whether the full assertion or only that special case has been resolved.