Only if the person is a Canadian or Mexican citizen, the U.S. work is prearranged professional work in a listed Appendix 2 occupation, and the person meets that occupation's own credential rule. The corporate link between the plants is irrelevant to TN; it matters for L-1.
Which document decides it
The decisive record is the U.S. entity's description of the position. Read it for the profession it actually describes: a process engineer who redesigns line layouts and validates equipment is doing engineering work; a person whose week is spent scheduling and disciplining a shift is doing supervision.
Only the first fits the Engineer entry. Then confirm the credential that entry requires, a baccalaureate degree or a provincial licence, and check that the applicant holds it in her own name. If the plant wants her to keep a Québec payroll and reporting line, the intercompany arrangement must still show that a U.S.
entity has prearranged her professional services. Citizenship is checked last but it is absolute: a Canadian permanent resident cannot use TN no matter how good the letter is. Where any of these four facts is unclear, the fix is to obtain the true fact, not to redraft the letter around it.