I am a Tricare Preferred Provider. So for Tricare members no authorization is necessary (since July 2017) and the bills are sent to and payed directly by Tricare.
For all other U.S. insurances no direct billing is available. I will give you a bill to pay which you later submit to your health carrier for reimbursement.
No authorization (Überweisung) is required. The Gesetzliche Krankenkassen will cover the costs.
Please contact your private German insurance company to get the necessary forms and to confirm that psychotherapy is covered.