They should use the same ID with which they signed into messages.
If this doesnt work, try creating a contact card for that person if you dont already have one.
Sharing Screens
iOS Messages and Mac iMessages are cousins.
While both apps work similarly, Mac has an extra feature that iOS lacks: a screen sharing feature.
Below are steps on how to work around this and screen share in iPhone iMessage.
prior to beginning, double-check you have a Lightning cable.
One such app is Zoom, a video conference software.
Zoom is one of the most flexible and easy-to-use video conference applications out there.
It also has a share screen option embedded in it.
When sharing your screen, be careful with the information you are displaying in the background.
Your safety is your responsibility.
Share your screen with only people you trust.