Provide the revised duties and arrangement for assessment before assuming the original L-1B plan covers the change.
Describe the change in practical terms
Explain who assigns the work, what knowledge is used and where the applicant would work. Identify the intended effective date and any immigration steps required. A customer’s request to continue support is not itself permission to do so.
Fix the effective date before the work changes, not after. A revised assignment assessed in advance can be adjusted; the same assignment assessed once it is under way can only be explained. Ask the employer to name the date the new duties begin and to hold that date until the assessment is complete, and put the request in writing so the sequence remains visible later.
Where a client is pressing for continuity of support, the pressure is commercial and does not alter what is authorized. Check the remaining time in status when planning the change as well, since a new phase beginning close to the general five-year L-1B maximum may call for a different route rather than an extension of this one. Raising that question while options still exist is the difference between a plan and a scramble.
Keep a note of when the assessment was requested and when the answer arrived; that pair of dates explains a gap far better than a later recollection of it.