Contemporaneous internal records that show the knowledge exists, belongs to the company and lives with this employee: formulations or specifications, training and development records, project files, confidentiality agreements, and an explanation of how the American assignment uses that knowledge rather than general skill.
Records made at the time beat descriptions written now
The weakest specialized-knowledge files are the ones assembled entirely after the decision to transfer. A letter asserting that an employee has unique expertise is the least persuasive document in the set, because it was written for the petition. What persuades is material that already existed: dated development notes, internal manuals bearing his name, records of the training the company gave him and the training it gives others, patents or trade-secret registers, and the confidentiality terms in his employment contract.
French-language documents need complete certified English translations under the general evidentiary rule. Hypothetical example: a dairy-genetics data analyst is put forward on the strength of a two-page resume and a manager's endorsement, with no internal documentation of the models she built or the training she received, and the request for evidence asks for precisely the material nobody kept. The practical answer is to begin keeping that material from today, because the next transfer will be judged on whatever records exist by then rather than on regret about the last one.