Fusion system-relatively weakly closed is not finite-intersection-closed

This article gives the statement, and possibly proof, of a subgroup property (i.e., fusion system-relatively weakly closed subgroup) not satisfying a subgroup metaproperty (i.e., finite-intersection-closed subgroup property).This also implies that it does not satisfy the subgroup metaproperty/metaproperties: Intersection-closed subgroup property (?), .
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Statement

Suppose $p$ is a prime number. Then, we can have a finite $p$-group $P$ (so, $P$ is a group of prime power order where the prime is $p$) and subgroups $H,K$ of $P$ such that both $H$ and $K$ are fusion system-relatively weakly closed subgroups of $P$ but $H\cap K$ is not a fusion system-relatively weakly closed subgroup of $P$.