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It is basically possible for you to return to Germany to do a doctorate as long as you have been promised a position as a doctoral student. However, it is not as straightforward if you have been living in Germany (for another purpose) and then decide to pursue a doctorate, as this would entail a change in your reason for residence.
After completing a degree in Germany, it is generally only possible to do a doctorate if
The general prerequisites apply (e.g. valid passport, proof of means of subsistence, health insurance coverage) for the issue of a residence permit.
Whatever the case, you must make an informal application to the Immigration Office.