During the offer discussion, before the letter is finalized. Once it has been issued and accepted, changing it means going back to a company that considers the hiring complete, which is a different and less comfortable conversation.
The draft stage is the only easy stage
Recruitment moves quickly at the end. There is usually a short window between the verbal offer and the written one in which a candidate can ask for the letter to describe the period and the duties accurately, and almost nobody uses it because asking feels presumptuous. It is not: employers issue letters expecting some negotiation, and a request about how the role is described is far less contentious than one about money. Use that window deliberately. If the letter has already been issued, ask for a revised version promptly rather than after you have resigned elsewhere, and be honest with the employer about why the wording matters to the process.
Hypothetical example: Noor, an interior designer, is asked to start an American project three weeks after the verbal offer. An opening assessment works backward from the intended entry date and identifies who must provide the employer letter, credentials, and any licence evidence. The project schedule and written offer settle whether the proposed dates are realistic. Request missing records first, then allow time to compare duties with the professional category before making irreversible employment decisions. Timing problems usually begin when a candidate resigns or relocates on the strength of a verbal assurance and discovers that the supporting letter describes a different role. A revised start date is often less disruptive than defending an avoidable inconsistency.