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Every civil marriage with was done at the Registrar's office (Standesamt) in Germany is registered in the respective Standesamt. If a german citizen is getting married abroad, the marriage may be registered upon request at the local Standesamt. If none of the partners is German, and the marriage happened outside Germany the marriage can not be registered in Germany.
Foreign marriages are generally regarded valid in Germany if the legal provisions regarding marriage of that foreign state were abided by. There is no special procedure or authority empowered solely to recognize marriages entered into abroad. The question of whether a marriage is valid is therefore always only a preliminary issue in connection with other administrative acts (e.g. change of name, change of entry on one's tax card, etc). This preliminary issue must be determined by the agency responsible at its own discretion.
In reality: If the Meldebehörde / Standesamt / Ausländeramt regarded your marriage as valid once, most likely you'll have no more problems regarding the validity in Germany)
I hope my answers were helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.