If they enable iCloud sync for messages it will update everywhere, they can also make sure they have Text Message Forwarding selected on their phone. They’ll get the messages in a timely manner (I get mine at the exact same time as my phone) and read messages will be reflected in all locations. I’ve been using iMessage on a Mac, iPad, and iPhone in some combination or other since the feature was offered, and the only issue I’ve ever had with sync was when I did a clean setup on a new Mac instead of a setup from backup. The above options weren’t selected.