My iPhone and computer SENT messages are not syncing?

My iPhone and computer SENT messages are not syncing?

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From the iOS Device(s):

Open "Settings" on the iOS device and tap on "Messages"
Scroll down and tap on "Receive At" which is usually followed by a phone number or email address
Tap the "Use your Apple ID for iMessage" button at the top and sign in
Exit out of Settings and return to the Mac briefly.

From the Mac(s):

Double-check the Apple ID used in Messages for Mac is the same as the iMessage setup in iOS
This problem seems to mostly effect users who set up iMessage on the iOS device a while back but based the delivery and caller ID on their phone number and not their Apple ID. Because Messages for Mac uses an Apple ID and not a phone number, the messages won't sync. Simple cause, simple solution.

Similarly, if you discover that iMessages aren't syncing between multiple iOS devices, be sure to use your email address and Apple ID as caller ID and all should be working as intended.

Things still aren't working? Try this:

Confirm Your Apple ID Mobile Phone Number
Another possible solution is to confirm your mobile phone number with your Apple ID. This has been reported to be a fix for some users who have persistent issues after the above sequences turn up blank.