Use the genuine operative arrangement and explain the change. An earlier proposal should not be presented as the final scope if the parties agreed to different work.
Keep the negotiation history intelligible
Identify who can confirm the actual duties, compensation and intended period. Preserve relevant versions rather than quietly selecting the one that sounds more professional. The supporting letter should match the work the applicant will really perform.
Bring a passport confirming citizenship, the job offer with a detailed duty description, transcripts and licences, a resume covering relevant experience, and any existing U.S. immigration history. Ask the employer to avoid two habits that create problems: padding the description with duties from other roles in the group, and describing the position as a contract engagement because that is how the group pays other consultants. If a staffing agency and an end client describe the assignment differently, ask them directly to reconcile the discrepancy rather than picking whichever version looks better. A payroll register shows which entity actually compensates the professional; a signed services agreement shows which one directs the work; a degree transcript or an entry in a licensing body's register shows whether the qualification attached to the listed profession is met on its face.