Fusion system-relatively weakly closed not implies isomorph-normal

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., fusion system-relatively weakly closed subgroup) need not satisfy the second subgroup property (i.e., isomorph-normal subgroup of group of prime power order)
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Statement

It is possible to have a group of prime power order $P$ and a subgroup $Q$ of $P$ such that $Q$ is a weakly closed subgroup of $P$ relative to any fusion system on $P$, but $Q$ is not an isomorph-normal subgroup of $P$: there is a subgroup of $P$ isomorphic to $Q$ that is not a normal subgroup of $P$.

Thus, $Q$ is a fusion system-relatively weakly closed subgroup and hence also a Sylow-relatively weakly closed subgroup (?) of $P$ that is not an isomorph-normal subgroup.