My wife finished her Masters and has been working under OPT and has H1B approval. Now she has an opportunity to move to a non-profit research organization.

1. Does she need to get a visa stamped on her passport, before her new employer can transfer the H1?

Answer: That would not be required.

2. Is it a problem to transfer a H1b approved under the cap, to a H1 employer who is a non profit research organization?

Answer: No.

3. Her H1 starts from October, and does this affect the transfer of the visa?

Answer: No.