The tree antimagic conjecture for finite Abelian groups

Let $A$ be a finite Abelian group, and let $T$ be a tree. An $A$-antimagic labeling is an edge labeling whose induced vertex sums are pairwise distinct. Tree antimagic conjecture. A tree $T$ is $A$-antimagic if and only if $|T|\not\equiv2\pmod 4$. This conjecture is motivated by the obstruction that no tree of order congruent to $2$ modulo $4$ admits an $A$-cordial labeling. The source presents the assertion as an open conjecture for trees in general.