If your Outlook (or any desktop email client) is connecting to the mail server over POP protocol than this will not work.
POP is a protocol which works only on the Inbox. Its a dated protocol, whose job is to retrieve the mail from the server, download it to the client and let the client do all the mail management. Once the mail is POPPED off the server, it is the client software’s responsibility to manage the mail.
The user can create local folders to bifurcate the mail, define rules to automatically do this, etc. Mail sent from such accounts are sent via SMTP on the server and are stored on the Sent Items of the client.
The POP protocol does not support writing back to the server and hence the sent items cannot be written back to the server.
All this comprises the local mail store (PST files in case of Outlook) and needs to be backed up and maintained.
The above note suggests that if the user is OK to maintain the mail on their client PC (backups, etc), you may use the POP protocol.
However if you need to maintain your mail on the server and be in sync across multiple devices and clients, it is highly recommended to use the IMAP protocol for accessing your mail. The IMAP protocol is also very efficient and higher performing. Using this, all the IMAP folders are maintained in sync across all access clients and devices. This allows you to get a uniform view no matter what client you use. This includes the sent items as well.