Send the changed facts for review before relying on the earlier preparation. A new client assignment, different employer or materially different duties can raise questions that the original letter did not address.
Create a change log for the employer to confirm
Write down the original and revised worksite, duties, reporting arrangement and proposed start date. Keep any replacement offer next to the previous version, with the change date visible. Ask which facts affect the immigration plan and which supporting records need updating. This avoids the practical mistake of arriving with a polished letter describing a project that no longer exists. Completion of paperwork alone does not authorize starting employment.
An in-person application at a land border or preclearance facility produces a same-day answer with no visa required; an employer petition on Form I-129 takes longer but leaves a written record and a decision that can be reviewed before anyone travels or resigns. Where the employer needs cover in the interim, that is a staffing question to be solved separately rather than a reason to compress the immigration one, and saying so early usually produces a better conversation than discovering it after a second attempt.