Q: ipad messages do not sync with iMac when message sent from iMac

Hello allanfromalliston,

I'm sorry to hear you are having issues with Messages. If you are not seeing the same messages between Messages/iMessage on your Mac and iPad, you may want to make sure that the same accounts are set up on both devices correctly, as noted in the section of the following article labeled Use iMessage and FaceTime with multiple devices: 

iOS and OS X: Link your phone number and Apple ID for use with FaceTime and iMessage - Apple Support

Sincerely,

- Brenden