For Microsoft 365 shared mailboxes you need to contact IT to set the option.
otherwise, for the exchange webapp follow these steps:
- Log in to OWA of a mailbox you have send as/full access or send on behalf of permissions.
- Navigate to Options in the upper-right corner> See all options > Settings tab > Sent Items tab.
- Messages sent as this mailbox can be saved in the Sent Items folder of the:
- From mailbox;
- Sender and From mailbox;
- Sender mailbox.
The same options are available for messages sent on behalf of this mailbox.