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The claim of driving without a license can only be, if your wife need a German driving license for driving in germany.
During a temporary stay in Germany, your American driver's license is unlimited.
For permanent relocation to Germany the American driver's license is valid 6 months. Afterwards, a German driving licence must be granted.
If your wife permanently moved to Germany in April, the american driver's license would apply 6 month. Thus at the time of the accident.
As driving without a license constitutes a criminal offence, the police suspected must determine.
The public prosecutor decides whether it adjusts the thing or collects charges. The police must inform the Prosecutor about the determination.
You should explain that your wife came in April to Germany permanently and thus the American driver's license is valid until September.
I hope I was able to help.
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