You as an employer should always make a copy of student visas and DS – 2019 forms. Always follow visa expiration dates and status.
Program participants are fully authorized to work by the USA Government. They all own:
A J-1 visa is a non-immigrant visa issued by the United States to exchange visitors participating in programs that promote cultural exchange.
DS – 2019 Form
DS-2019 form is a "Certificate of Eligibility for Exchange Visitor (J1) Status" from the Department of State, which is an agency of the U.S. Government.
All participants must apply for and receive a Social Security Number by visiting their local Social Security office. Students who participate in the program for the second time already obtain valid SSN.
According to the program regulations, all J-1 students must have a medical insurance. You, as an employer, shouldn’t be worried about it.