Answer work-authorization questions accurately and directly. If the recruiter asks whether you currently or eventually require sponsorship, give the factual answer.

The international-student consulting recruiting guide explains why sponsorship policies can vary substantially by office and country.

You do not need to turn the entire conversation into an immigration discussion unless it is relevant. Be clear about your current status, future requirement, and any time limits you know.

If the office cannot sponsor the role, it is better to learn that early than to discover it after several rounds.

Recruiter asked me directly, so I just answered exactly what my status was.

Do not try to wordsmith around sponsorship. They need the real answer.