Medical Doctor, new Graduate in US. No VISA. Need Advice?

Hello my boyfriend just graduated with his medical degree. He is from the West Indies. He is here on a B1 Visa (Student Visa expired) He needs to begin his residency. Please, I humbly ask if anyone out there knows of any programs for educated professional doctors who want to work in the US or of any Hospitals that sponsor MD's on Visa in NY/NJ area. OR is there a way for him to work while he has a Visa? can he extend his Visa while he searches for a hospital. He is well spoken, kind, healthy, productive. He is very stressed out and at his wits end. I love him and really want him to stay. He wants to work and is clearly qualified. This is no joke. Again, I humbly ask you for your suggestions on how this deserving man can remain in the US and work as a medical doctor. In advance, I thank you.