Hello mannes2111,
We have a great support article that might help with this. Please take a look at it here: Set up your replacement AirPods or charging case - Apple Support. Follow this guidance:
"Set up your AirPods or charging case
- On your iPhone, iPad, or iPod touch, go to Settings > Bluetooth and tap the Information button
next to your AirPods. - Tap Forget This Device.
- Tap Forget Device, and tap again to confirm.
- Put both AirPods in your charging case.
- Open the lid and check the status light. It should flash amber.
- Press and hold the setup button on the back of the case for a few seconds. The status light should flash white.*
- Go to the Home Screen on your iPhone, iPad, or iPod touch.
- Open the case—with your AirPods inside—and hold it next to your iPhone, iPad, or iPod touch. A setup animation appears on your screen.
- Tap Connect, then tap Done.
* If the status light still flashes amber, connect the case to power, close the lid, and wait 20 minutes. Then open the lid and press and hold the setup button again for a few seconds until the status light flashes white."
We hope this helps. Let us know if we can assist with anything else at all. Take care.