G-ADMS conjecture on distinct partial sums in cyclic groups

Let $A\subseteq \mathbb{Z}_n\setminus\{0\}$. An ordering of the elements of $A$ determines partial sums by cumulatively adding the ordered elements.

G-ADMS conjecture. There exists an ordering of the elements of $A$ such that all partial sums are distinct.

This conjecture is the cyclic-group analogue related to the Alspach conjecture and was proposed for cyclic groups by Graham and by Archdeacon, Dinitz, Mattern and Stinson. The source proves it for subsets of size at most $12$ in cyclic groups of prime order; the general statement remains open.