Germany holds discretion over recognizing refugee status originating from Greece.
In the European courts' decision, Germany isn't legally bound to consider asylum-seekers who've already been designated as refugees in another EU nation as such. An example of this was the Syrian woman who was initially granted refugee status in Greece but then applied for protection in Germany. Due to the poor living conditions for refugees in Greece, which potentially posed a risk of inhumane or degrading treatment, the German court refrained from deporting her back to Greece.
Yet, the woman wasn't recognized as a refugee in Germany; instead, she was only granted subsidiary protection. Subsequently, she appealed to the German courts to upgrade her status to a full refugee. The Federal Administrative Court then consulted the European Court of Justice (ECJ) regarding Germany's obligations in such instances.
As a result, the ECJ stated that EU countries are under no obligation to adopt the refugee status granted to asylum-seekers in other EU countries. They can, but Germany chose not to. Consequently, the responsible authority must reassess her case.
However, they should communicate with the responsible authority of the initial EU country, in this case, Greece, considering their initial decision during the examination of the application. In the specific case, the Federal Administrative Court is currently deliberating on her status, factoring in the ECJ's legal opinion.
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Despite the Syrian woman having refugee status in Greece, Germany was not obligated to recognize her as a refugee due to a ruling from the European Court of Justice. Regardless of her initial status in Greece, Germany granted the woman subsidiary protection rather than refugee status and she later appealed for an upgrade.