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The Aufnahmeschein (White Paper) is handed out at the Ankunftszentrum (Reception Center) and shows your personal details and what kind of documents you gave away at registration.
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The green Ankunftsnachweis (AKN) confirms that you have been registered as an asylum seeker in Germany. It is also handed out at the Ankunftszentrum and allows you to obtain state benefits (accommodation, medical care, food).
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The green Aufenthaltsgestattung (AG) gives you the permission to stay in Germany until the end of your asylum application. It is not handed out at the Ankunftszentrum but at your 1st interview (Aktenanlage) at the BAMF (Migration Office).