Every subgroup of a finite Abelian group is potentially characteristic

Statement
Let $$G$$ be a finite Abelian group and $$H$$ be a subgroup of $$G$$. Then, $$H$$ is a potentially characteristic subgroup of $$G$$. In other words, there exists a group $$K$$ containing $$G$$ such that $$H$$ is a characteristic subgroup of $$K$$.