My messages between iPhone and MacBook Air are not syncing

Several days ago, I called Apple Support. The phone answered immediately. My issue was that messages on my iPhone and MacBook Air would not share, even when I refreshed iCloud. After Apple support, it worked briefly, except that images were not shared. Now the whole thing is back to not sharing. This is a known issue. It sure would be great if someone in Apple's upper management would start to address this issue and update the operating systems to put a stop to this long-time issue. I love my MacBook, but the Apple messaging system is no good; it appears to be stuck somewhere around 1998.

[Re-Titled by Moderator]

Original Title: messages not sharing across devices