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妹妹一家F4移民，妹妹 （Principal applicant）必须住在美国吗才能保住她全家的绿卡吗？

-Irrelevant.

妹妹想留下她的儿子在美国上高中，然后她回中国，因为在中国的父母需要照顾。 妹妹的儿子（derivative applicant）能独立在美国吗 （i.e. keep his green card) after his mom (principal applicant) goes back to China? 

-Yes, the mom leaving does not affect the kid's green card validity 

另外，绿卡持有者必须一年内在美国住几个月才能keep绿卡？

-At least 6 months evey year. Of course, it is fine occasionally to stay outside US for more than 6 months but less thna one year. If you need to stay outside US for more than one year, you need to apply for reentry permit.

谢谢！