Please send me a copy of the following documents and we can move forward. As a reminder, this is not to start the transfer process, this is to simply verify your H1B is valid and transferable at this time.
Copy of your last pay stub
Copy of I-94 card
Copy of H1B approval notice
-I think it is reasonable for the job recruiter to ask for this kind of information because they have to know whether you have a legal status and are qualified to work for a new employer. Without this information, they may not serve for you.
