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F2 to Green Card Process
The F2 Dependent Visa is a nonimmigrant permit, meaning that it cannot lead to obtaining a Green Card, but you may apply for a change of status while in the U.S. on this visa.
While you can find a U.S.-based sponsor to change your status, you cannot seek full-time employment or education until you get a different permit.
As long as you do not violate the terms of your visa, you should be able to change your immigrant status without leaving the U.S.
If you decide to travel abroad before you receive your new visa and after your F2 permit expiration date, you may not be able to re-enter the country.