Three things at once: a qualifying parent, branch, subsidiary or affiliate relationship between the two companies, both of them actively doing business, and one continuous year of qualifying employment abroad with the group within the preceding three years. The American role must then be managerial or executive in substance.
Corporate facts first, personal facts second, title last
Applicants usually arrive with the personal half prepared and the corporate half assumed. Reverse that order. Establish which of the four recognised relationships exists and produce the documents that show it, then confirm both entities are trading rather than dormant, then reconstruct the year abroad from records that already existed.
Only after those three are settled does the job description matter, and it should be written to describe real duties rather than to satisfy a definition. Hypothetical example: a poultry-operations director from the same area assumes she qualifies because her employer and the American company share an owner, but the American shares are held by a holding company two levels above her employer, and nobody has drawn the chain. Until that ownership path is on paper with percentages at each level, there is no way to say which relationship exists or whether one exists at all.
Drawing that ownership chain is a morning's work with the corporate records, and it decides whether there is a case at all rather than merely how strong one is.