The petitioning employer, the U.S. affiliate of the Canadian company, files Form I-129 and pays the fees in the USCIS G-1055 schedule. The customer is not the petitioner and should not be paying the specialist or directing the work.
The petitioner pays, and that fact supports the case
Hypothetical example: the U.S. customer is willing to pay for the integration project but wants nothing to do with immigration filings. That is the correct arrangement. The U.S. affiliate that employs the specialist files the petition and pays the Form I-129 fee, any additional fee applicable to L petitions, and premium processing if it chooses, all per the current G-1055 fee schedule. The customer pays the company for the deliverable under the services agreement. Keeping the money flows this way supports the requirement that the specialist is not labour for hire: salary and instructions come from the petitioner, not the client. Other costs include translations of French records, legal fees and relocation, which the company should budget separately. If the customer insisted on paying the specialist directly or supervising them, the structure would need to be rethought before filing.
Hypothetical example: a grain-dryer controls technician is transferred for a short installation, and the employer treats the case as a travel expense only. Prepare a filing budget that separates the current petition charge, any required employer fee, optional expedited processing, dependent costs, visa costs if applicable, translations, and ordinary project travel. The current USCIS schedule and the petitioner's filing history determine the immigration amount; a prior L case may have been charged differently. Decide whether the job needs an expedited adjudication before paying for one, and keep the commercial deadline independent from the immigration budget. A clear allocation between the U.S. and foreign companies also helps prevent later disputes over who arranged the assignment.