Order in case of accident damage regulation (accident from the other)

Hello, my wife had had an accident before Christmas, and she was driven up in the city from behind. She has a BMW 3 Series E46. The woman in the other car immediately said that she was to blame and she and my wife described the accident process on paper, changed the phone number, address, name and so. We then called the opposing insurance the next day, and made the report at BMW branch office and on the estimate stood 1600 EUR anything. The insurance company has now agreed that we can fix it. My question would be, should we have it repaired first and send the invoice or can we first ask for the payment from the insurance company? I have searched, and have not found a specific order. Could you explain it to me for a moment? Thank you!