Weakly closed implies relatively normal

Statement
Suppose $$H \le K \le G$$ are such that $$H$$ is a fact about::weakly closed subgroup of $$K$$ relative to $$G$$. Then, $$H$$ is a fact about::normal subgroup of $$K$$. In other words, $$H$$ is a fact about::relatively normal subgroup in $$K$$ with respect to $$G$$.