Identity functor controls strong fusion for saturated fusion system on abelian group

In terms of control of strong fusion
Suppose $$P$$ is an abelian group of prime power order. Suppose $$\mathcal{F}$$ is a saturated fusion system on $$P$$. Then, the identity functor (i.e., the functor sending a group to itself) is a conjugacy functor that controls strong fusion on $$P$$.

In the language of resistant
Any abelian group of prime power order is a resistant group of prime power order.

Group theory version

 * Identity functor controls strong fusion for abelian Sylow subgroup