Inner automorphisms of non-commutative analogues of the additive group of rational numbers

It is proved that the inner automorphisms group of the group $A(m,n)$ are characteristic subgroup in $Aut(A(m,n))$ for all $m > 1$ and odd $n\geq 1003,$ where the groups $A(m,n)$ are known non-commutative analogues of the additive group of rational numbers.