That the U.S. entity is a parent, subsidiary, branch or affiliate proven by ownership records; that she has a continuous qualifying year with the group; and that the U.S. role will be primarily managerial or executive with real subordinates or an essential function.
Three facts, all held by the employer
The transferee rarely owns the evidence an L-1A petition depends on, so the requirements are best understood as questions for the employer. First, the corporate relationship: the Shannon company and the Texas entity must be linked as parent and subsidiary, branches of one company, or affiliates under common ownership and control, and the share registers must show it. Hypothetical example: a logistics firm's two founders each hold half of the Québec company and half of the Texas affiliate; that is a qualifying affiliate relationship.
Second, the year abroad: the manager must have worked for a group entity for one continuous year in the last three, in a managerial, executive or specialized-knowledge capacity, proven by payroll. Third, the U.S. role: primarily managerial or executive, with authority over people or an essential function, not a working supervisor.
Both entities must be doing business. The manager's nationality is irrelevant to L-1A, which is why it suits mixed-nationality Shannon households.