Chronologically: how the process was developed, how the engineer acquired knowledge of it, and then how the U.S. subsidiary will use it. Corporate relationship and payroll evidence follow as the supporting layer.
Tell the story in the order it happened
A petition assembled as a pile of exhibits forces the officer to reconstruct the case. A petition assembled as a sequence makes the conclusion obvious. Begin with the company: what it builds, the plants it has commissioned, and where the proprietary procedure fits. Then the procedure itself: the controlled document with its revision history, showing the engineer as author or principal contributor, with dates. Then the engineer's history: hire date, project assignments, training he delivered to colleagues, and payroll covering the qualifying year. Then the U.S. need: the equipment sale, the commissioning obligation, why the subsidiary's local staff cannot perform it and what training they will receive. Finally the corporate layer: share registers, articles and evidence both entities are operating. A short cover letter with a table of contents lets the officer find each element, and every assertion in the letter should point to a page in the exhibits. Avoid marketing language; use the words the company actually uses in its procedures.
Hypothetical example: a blast-freezing equipment maker needs its thermal-control specialist at a U.S. affiliate. Build the exhibits in time order: the original design records, the specialist's project work, the foreign payroll year, and the U.S. installation scope. The revision log settles the specialist's connection to the method, while the equipment contract explains the business need. If customer-site access is involved, add the control provisions showing the petitioning group, rather than the customer, directs the assignment.