Polish LCA groups are strongly characterizable

Positively answering a question of Gabriyelyan [21, Problem 2.13], we prove that for every second countable locally compact abelian group G   and every continuous monomorphism s:G→Ks:G→K into a compact metrizable abelian group K  , there exists a sequence of characters (un)(un) of K   characterizing the subgroup s(G)s(G), i.e., s(G)s(G) coincides with the subset of those elements k∈Kk∈K such that (un(k))(un(k)) is a null-sequence in the circle group TT.