Documents that show authority being exercised, not asserted. Organizational charts naming real subordinates with their own job descriptions and salaries, payroll registers, budgets she controls, and decisions she has taken without approval from above carry the claim. A title in an offer letter carries nothing.
Show the authority working, then describe it
The strongest files read backwards: they begin with artefacts generated in the ordinary course of business and only then summarise. Hypothetical example: for Mireille that means the Quebec chart with names, positions and reporting lines rather than boxes; the payroll register proving those people exist and are paid; the capital request she approved for a new mixer; the supplier contract she signed; the disciplinary decision she took. For the American side it means the same categories projected forward and dated, with a hiring plan showing which positions will exist by which month and what each will cost.
Where the claim rests on managing an essential function instead of managing staff, the function has to be named and its significance to the organization explained, with the seniority of her position within the structure made visible. A description written in the language of the regulation without any of this underneath it is the most common reason a genuinely managerial role is refused.