One would first need to establish domicile; this is determined by where the parties pay taxes, where they would qualify for in state tuition,and where they vote, for example. If both spouses are overseas, then they can file in the state where they last lived for the 6 months prior to deployment.
To file for divorce in Germany (assuming one becomes a legal resident), the couple must have lived apart for at least one full year to get an uncontested divorce. The court will have jurisdiction over all issues except for military pensions, as only a US court can divide that.
Here is some information while divorcing overseas:
Also, a spouse can consent to jurisdiction, so for example, if one spouse files from their home state, the other can consent to that court's jurisdiction so that the divorce can proceed. One would need to work with an attorney to help facilitate the divorce process from overseas.
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Information provided is for educational purposes only. Consultation with a personal attorney is always recommended so your particular facts may be considered. Thank you and take care.