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我儿子拿到了新的DS－2019表，是不是就意味着即使他原来的DS－2019表已过期，他仍可以用新的DS－2019表合法地留在美国，
-Yes if the DS-2019 is based on your spouse's J-1 status and your child was issued a new SEVIS ID. So, check it with your school to make sure your son's new J-2 has been put into SEVIS. Not need to file I-539.

而不需要回国重新申请J-2签证
-Depends on whether the school put the J-2 extension to the SEVIS with a new SEVIS ID based on your spouse J-1. If no, your child may need to go to China to get the J-2 visa.