Clarify who will obtain and pay for new employer records, credential work and professional review. Government charges and professional fees are separate from the employer’s commercial cost of changing the role.
Identify the purpose of each new expense
Ask whether a requested evaluation, translation or document is needed for the actual profession or merely duplicates material already available. Verify current official fees rather than reusing an old quotation. Spending on additional paperwork does not make a mismatched assignment eligible. Keep the employee’s travel and family expenses visible so a narrow filing estimate is not mistaken for the total cost of accepting the revised job.
Having the employer file Form I-129 with USCIS in advance involves the petition fee in the current fee schedule and, if speed matters, the optional premium-processing fee; the applicant then presents the approval notice at the border. A corrected letter and a registry extract are ordinary administrative costs; a genuine change of employing entity may require a fresh request, and possibly a Form I-129 petition, with its own government charges and preparation time.