Before the new work starts. A material change assessed in advance is an administrative step with a known cost; the same change assessed afterwards is a period during which the person was doing work the file never described. Extensions should also be started well before the admission expires.
Sequence the paperwork ahead of the new duties
Two timing habits prevent most difficulties in this category. The first is to treat any proposed change in the work as something to resolve before accepting it, not after. A client asking a consultant to step into an operating role is asking a question with an immigration answer, and that answer is much cheaper before the person has spent three months in the new position.
The second is to watch the two calendars that run in parallel: the engagement's end date, which is commercial, and the admission's end date, which is not, and which does not extend itself because the work continues. Extensions take preparation and should begin months ahead. Where a consultant knows the pattern of their practice involves several clients a year, it is worth deciding in advance which changes will be treated as material, so the decision is not remade under pressure each time.