Yes. An L-2 spouse is authorized to work incident to status and does not need a separate employment authorization document to begin, though many employers ask to see the endorsed admission record. He may work for any employer, including the subsidiary.
The spouse's authorization travels with the status
The spouse of an L-1A manager is admitted in L-2 status, and USCIS treats L-2 spouses as employment-authorized incident to that status. In practice the spouse's Form I-94 is annotated to show the spousal status, and that record serves as evidence of authorization for a U.S. employer's Form I-9. He may take any job, including one at the subsidiary, and he may also choose not to work. Children in L-2 status may attend school but cannot work, and they cease to qualify as derivatives at twenty-one, which matters if the assignment is expected to run several years. Each family member needs a valid passport and evidence of the relationship, such as the marriage certificate and birth certificates. The spouse's Canadian employment history has no bearing on the L-2 application itself.
Hypothetical example: a ceramic-tile importer transfers its Canadian general manager with a spouse and a nineteen-year-old child. The family review produces separate files: civil records prove the relationship, passports support travel, and the principal's approval and admission record establish the derivative period. An L-2 spouse normally has work authorization through that status, with the annotated admission record serving as evidence; the child may study but lacks work permission and will cease to qualify at twenty-one. The family's real decision is whether the child's education timetable fits the manager's temporary assignment and the remaining L-1A time.