Yes, those are the requirements for foreign earned income exemption. Regarding income from an international organization, the IRS states that if you are an employee of a foreign government (including a foreign political subdivision) you may be able to exempt your foreign government compensation from U.S. income tax either under a provision, if one exists, in an applicable tax treaty or other international agreement, or by meeting the requirements of U.S. tax law.
Income for employees of foreign governments or international organizations.
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