Permissions in any context are required in order to access the resources and services for maintenance / sanity check purposes, compliance purposes and in some times requires for a central administration.
With Office 365 mailbox architecture it has 3 different types of permission where we can;
Access Other’s Mailbox
Send Email on Someone’s behalf as Send-As or Send-on-behalf.
Breakdown of Office 365 Mailbox Permission Types
Full Access Permissions
People with full access permissions can access the mailbox completely. You can assign these permissions either to a user mailbox or a shared mailbox itself. This gone be done through Graphical User Interface [GUI] from the Exchange Admin Center or also through PowerShell Command.
The full access permission lets a user log into the shared mailbox and act as the owner of that mailbox. While logged in, the user can create calendar items, contacts and tasks and read, view, delete and change email messages. However, users with full access permissions cannot send email from the shared mailbox unless they also have Send As permission.
Send As Permissions
People with this access can view and reply/send under their personal account, unlike full access users who can send messages under their shared mailbox identity. You will usually want to enable this permission. The Send As permission lets a user impersonate the shared mailbox when sending mail.
For example, if Mary logs into the shared mailbox firstname.lastname@example.org and sends an email, it will look like the sales department sent the email.
Send on Behalf Permissions
Allows the delegate to send messages from the mailbox or group. The From address of these messages clearly shows that the message was sent by the delegate
However, replies to these messages are sent to the mailbox or group, not to the delegate. Doesn't allow the delegate to read the contents of the mailbox. If you assign the Send on Behalf permission to a mailbox that's hidden from address lists, the delegate won't be able to send messages from the mailbox.
Sending a message as, or on behalf of, a person
To send a message as, or on behalf of, a person, proceed as follows.
From within Outlook, click New Email.
A new Message window opens, with your email address in the From field.
In the new Message window, click, From, and select the required sender email address from the list of sender email addresses shown.
3. If the required address is not shown, then:
Click, Other E-Mail Address.
The Send From Other E-Mail Address dialogue box appears.
In the text box, start typing the required email address.
Enter the address which has the required permission and send the email.