  Consider the strong subordination of a multivariate L\'evy process with a
multivariate subordinator. If the subordinate is a stack of independent L\'evy
processes and the components of the subordinator are indistinguishable within
each stack, then strong subordination produces a L\'evy process, otherwise it
may not. Weak subordination was introduced to extend strong subordination,
always producing a L\'evy process even when strong subordination does not.
Here, we prove that strong and weak subordination are equal in law under the
aforementioned condition. In addition, we prove that if strong subordination is
a L\'evy process, then it is necessarily equal in law to weak subordination in
two cases: firstly, when the subordinator is deterministic and secondly, when
it is pure-jump with finite activity.
