Before. Once instructions are issued and funds move, unwinding an entity mismatch is harder than correcting it on paper. Category and chargeability review can begin early, and does not have to wait for the gift stage. Note that raising a question with the employer or the agency does not pause any deadline you have been given.
Sequencing the switch against the steps you cannot control
Map the proposed entity change against the steps already completed and the instructions still outstanding. Eligibility in EB-1 or EB-2, admissibility and visa availability remain required; review them before committing the gift. Follow any official update or replacement-filing instruction and check inconsistent notices independently.
A description of processing in weeks does not settle when the changed case will be ready. There is a natural order here and it is worth defending against pressure to compress it. The entity question is answered first, because everything downstream is described against it.
Category eligibility and admissibility are reviewed next, since they belong to the applicant rather than to the employer and can run in parallel. The payment steps come last, because they are the ones that cannot be taken back. Hypothetical example: a group aligns the sponsorship change with the start date it promised the U.S.
customer of a packaging-line installer, and the payment stage arrives before anyone has confirmed which entity is sponsoring. Raising a question with the employer or with the agency does not pause a deadline you have been given, so ask for the deadline itself to be moved rather than assuming a query has that effect.