Strict characteristicity is strongly join-closed

Statement
Suppose $$G$$ is a group and $$H_i, i \in I$$, is a collection of strictly characteristic subgroups of $$G$$, the join of subgroups $$\langle H_i \rangle$$ is also a strictly characteristic subgroup of $$G$$.

Related facts

 * Endo-invariance implies strongly join-closed