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妹妹一家F4移民，妹妹 （Principal applicant）必須住在美國嗎才能保住她全家的綠卡嗎？

-Irrelevant.

妹妹想留下她的兒子在美國上高中，然後她回中國，因為在中國的父母需要照顧。 妹妹的兒子（derivative applicant）能獨立在美國嗎 （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，綠卡持有者必須一年內在美國住幾個月才能keep綠卡？

-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.

謝謝！