Trouble-shooting screen sharing over messages
I have a 2015 iMac, FusionHD, macOS 12.1.2.
I am trying to help seniors dealing with problems with their Macs.
90% of the time I am able to use Messages.app to view and control their Macs.
10% of the time I will extend the invitation to share screens, they will never receive it, and the attempt times out with something like: John Doe is not available for screen sharing.
I will carefully walk these folks through the process of making the proper changes to Sys Prefs > Sharing by following Apple's instructions to the letter, but the same thing happens: they never get the invite.
However, when we turn it around and they send me an invite to view their screen, it works, but of course it's not possible to control their screens and I have to go through the laborious, time-consuming process of "Click there, no, not there, to your left, etc.".
I have searched everywhere for an answer to this question but came up empty handed.
Please, can anyone help?