On my iPhone, I deleted and reinstalled the e mail account I'm using as a test and here are the results. Today I'm testing this with my iPhone5 and MBP. BTW, I appreciate your input on this as the subject has sort of strayed from general syncing to an iPhone related quirk and I don't want to upset the community forum! 😁
Using the test IMAP e mail account, when I send e mail to this account it is received across all devices (MacMini, MBP, and iPhone5) as expected.
If I open the e mail on my MBP I do notice that it also becomes marked as read on my iPhone, and vice versa so that sync is happening.
If I delete a read e mail message from either my MBP or MacMini the message does eventually get deleted from the iPhone (takes about 30 seconds or so) with nothing more than pressing the delete icon in Mail.
HERE IS THE ISSUE:
If I open a new message on my iPhone it does get marked as read on the MBP but when I press the TRASH icon I get the message that, "The message could not be moved to mailbox TRASH", however, the message is removed from the inbox on the iPhone. If I go into Accounts (directly below the list of mailboxes) > choose the email account in question > select Inbox > there is the message that I tried to move to Trash. I have to open that message > select the Folder icon to Move This Message to a New Mailbox > and then move it to the Deleted Messages folder. Once I've done this on the iPhone then the message does get deleted from the MBP inbox and ends up in the MBP Trash as you would expect, ditto on the MacMini. Also, the other test message that I deleted from the MBP, and that was deleted on the iPhone, also showed up in the Deleted Messages folder on the iPhone which probably makes sense. So am I crazy or just missing a setting related to deletion of messages on the iPhone!??
Thanks for your input.