My AirPods case and led turn green for awhile and turn off

You may get better and prompt responses if you may kindly provide the iPhone Model that you have and the iOS version if it is known to you.

AirPods Help

1. If one of your AirPods isn't working - Apple Support
2. If your AirPods won't connect - Apple Support
3. Identify your AirPods - Apple Support
4. AirPods Support
5. Connect and use your AirPods
6. How to Find Lost Apple AirPods
7. If your AirPods are lost - Apple Support
8. Replace an AirPod or charging case - Apple Support
9. AirPods Repair - Official Apple Support
10. Clean AirPods: Get a flashlight and a toothpick and clean the right AirPod connector in your case then clean the end of the right AirPad. After doing so put them both in the case, leave the lid open, press and hold the button on the back of the case until the light flashes.