Finite normal implies image-potentially characteristic

Statement
Suppose $$H$$ is a finite normal subgroup of a group $$G$$. Then, $$H$$ is an image-potentially characteristic subgroup of $$G$$: there exists a group $$K$$ with a surjective homomorphism $$\rho: K \to G$$ and a characteristic subgroup $$L$$ of $$K$$ such that $$\rho(L) = H$$.

Facts used

 * 1) uses::Finite normal implies amalgam-characteristic
 * 2) uses::Amalgam-characteristic implies image-potentially characteristic

Proof
The proof follows directly from facts (1) and (2).