Sent messages when using IMAP
Why a message you sent from one device does not appear on the others.
IMAP keeps your mail on the server, so every device shows the same folders. Sent messages are the usual exception. Many mail programs save their own copy on the computer that sent the message, rather than in the Sent folder on the server.
The result is that mail you send from your laptop never appears in webmail or on your phone.
Saving sent mail to the server
Open your mail program's account settings and find the option that controls where sent mail is stored. Set it to the Sent folder on the server rather than a local folder. The wording varies, but most programs describe it as storing sent messages on the server or in an IMAP folder.
If the server's folders do not appear in that list, the account's root folder path is usually wrong. Correcting it lets the program see the Sent, Drafts and Trash folders that already exist in your mailbox.
Clients that need no setting
Zimbra Connector for Outlook, Zimbra Desktop and Zimbra Mobile copy sent messages to the server on their own, so there is nothing to configure.
POP3 is the opposite case. A program collecting mail over POP3 usually cannot save sent messages to the server at all, which is one more reason to use IMAP.
Messages you have already sent
The setting applies to new messages only. Older sent mail stays where your program first put it. To bring it across, drag it from the local folder into the Sent folder on the server. Your mail program then uploads it to your mailbox.