Weak subset-conjugacy-determined subgroup

Definition
Suppose $$H \le K \le G$$ are groups. We say that $$H$$ is a weak subset-conjugacy-determined subgroup in $$K$$ if any two subsets of $$H$$ that are conjugate in $$G$$ are conjugate in $$K$$.

Stronger properties

 * Weaker than::Subset-conjugacy-determined subgroup

Weaker properties

 * Stronger than::Weak normal subset-conjugacy-determined subgroup