Airpod Pros disconnect while i Share screen on facetime

Hello and welcome to Apple Support Communities, iloverm,

We understand that whenever you share your screen while on FaceTime, your AirPods disconnect. We'd be happy to help you troubleshoot.

Since this is not how your AirPods are supposed to be behaving, try resetting your AirPods using the steps here: How to reset your AirPods and AirPods Pro - Apple Support

1. "Put your AirPods in their charging case, and close the lid.
2. Wait 30 seconds.
3. Open the lid of your charging case.
4. With your AirPods in your ears and connected to your iPhone, iPad, or iPod touch, go to Settings > Bluetooth, or Settings > [your AirPods], and tap the More Info button  next to your AirPods. If you don't see your AirPods in Settings > Bluetooth or in Settings > [your AirPods], just go to the next step.
5. Tap Forget This Device, and tap again to confirm.
6. With the lid open, press and hold the setup button on the back of the case for about 15 seconds, until the status light on the front of the case flashes amber, then white.*
7. Reconnect your AirPods: With your AirPods in their charging case and the lid open, place your AirPods close to your iPhone, iPad, or iPod touch. Follow the steps on your device's screen.

AirPods can be associated with one Apple ID. If you want to use AirPods (3rd generation) or AirPods Pro (1st or 2nd generation) that someone else has used, they first need to remove the AirPods from their Apple ID."

Regards.