Outlook 365 and Cox IMAP account not synchronizing across multiple PCs and Macs

Is Outlook 365 the only email client between all the computers?  Also, what are you using for your incoming server? Last, maybe try this? 

Thank you for responding. Yes, Outlook 365 is the only email client. The account is configured as follows:

incoming: imap.cox.net, port 993, use SSL to connect

outgoing: smtp.cox.net, port 465, use SSL to connect

In the Advanced Settings, for the Trash folder, I am using the "Move deleted messages to this folder" but never delete. I will try settings in the post you referred to i.e. select "Mark messages as deleted" and "Do not automatically delete messages" and see if that helps. 

Unfortunately the option "Mark messages as deleted" results in deleted messages not appearing in the Trash folder (basically they are gone) so that is not an option. Would you have another suggestion maybe?

Try another email client like thunderbird?

Unfortunately that is not really an option. The key question remains, how come GoDaddy IMAP and GMail IMAP work properly with Outlook 365 and Cox IMAP does not?

Since I have these accounts are configured exactly the same in Outlook, it is very puzzling why there is different behavior with the same email client software. Could it be that Cox has IMAP implemented differently than GoDaddy and GMail?

Outlook User said:
Unfortunately that is not really an option.

You can't download and try another client to isolate? If not, I don't know of any other way to help. Could be issue with account, Imap server, firewall,etc. If it doesn't work with another client, then I would try with a new Cox email address. If it does it gets alot more complicated with SSL sessions by telnet and watching the traffic route. 

I (incorrectly) interpreted your initial response as a suggestion to give up on Outlook 365. Temporary trying the Thunderbird email client for troubleshooting reasons to see if it behaves the same or not is not a problem, of course. Give me a few days to experiment and I will get back to you.

I installed Thunderbird and it found my email settings automatically (I doubled checked and the settings are correct). However, after it synchronized all email, my inbox shows all the messages I deleted in the past as unread (as well as lots of other messages that I deleted).

Because this is an IMAP account you would expect it should show the same inbox as Outlook 365 but it does not. Since this is a brand new Thunderbird install (I never had this application on my MacBook before) apparently these message were never deleted at the Cox server.

I originally (up to some time last year) was using Cox POP3 and then reconfigured Outlook to start using IMAP. Could it be that some left-over POP3 setting at the Cox server is causing this behavior?

Outlook User said:
my inbox shows all the messages I deleted

Even though they don't match, if you have a email that is in both placed, and you delete it, does it delete from both places?

Outlook User said:
was using Cox POP3 and then reconfigured Outlook

Did you move from Outlook POP3 to Outlook 365 IMAP? Or Outlook 365 POP3 to Outlook 365 IMAP? Basically, when even you change from POP to IMAP, you have to recreate the Outlook profile. This is because IMAP data is stored and downloaded differently and the profile won't sync the old email with the new email. If nothing else, Thunderbird backuped your email, so go in and disable the old profile in Outlook 365 and create another profile with same user/password settings. If that works, you can go in and delete the old account.