If your having problems getting your Apple Mail or Mac Mail to sync across your devices, I thought this might be helpful. It could be because you have your email accounts set up with POP rather than IMAP configuration. Try this solution.
I had set up my gmail account a long time ago (5 years) before I know the differnce between POP and IMAP. IMAP allows you to sync across devices... POP is OLD SCHOOL technology of the 90's. Now that I know better, and have more than one device I want to sync, so I want to change the settings in mac mail to convert the gmail emails from a POP account type to an IMAP accont type, but I cannot afford to loose all of my previous emails that I'd saved (100's of them), which is what will happend if you delete this account to start anew.
Odly, even after I set up the email as IMAP in gmail, it still did not update the account type in Apple Mail. Apparently this has to be done from scratch.
!.WARNING, BEFORE PROCEDING THROUGHT THE FOLLOWING, BACK UP YOUR MAC.!
What worked for me was actually rather simple, but to be safe BACK UP.
Note: It did dissassociate all of my "Signatures" but did not erase them from my email acconts (I have 14 email accounts with google apps). Your exprience could be different, so please ba safe and back up.
1) First I dissabled the existing email account in my Apple Mail program.
2) Then recreated the account from scratch as an IMAP.*
* Be sure to change the account to an IMAP in gmail first (Click the Gear on the right > Settings > Forwarding & POP IMAP > Disable POP then Enable IMAP
***Deactivating took the account out of view (hidden) but retained all of the saved emails from the past. At the same time it allowed me to recreate the account in Apple Mail from scratch and it auto pulled up the IMAP configuration, with the same gmail account I was using before set up as POP. ***
Now I'm left with the best of both worlds and all syncs perfectly.
Just don't forget and accidentally delete the inactive account, or you will lose ALL of the emails you saved during the time when the old POP email account was active.
Good Luck!