Send As permission is used when you need to give a user permission to use another recipient's email address in the From address. In order to give Send As permission to a user on Office 365 you need to use Windows PowerShell.
Windows PowerShell is a command-line shell and scripting language that can be used for managing various Microsoft's server products and in this case can be used to remotely manage Exchange Online.
To give Send As permission to a user use these cmdlets:
1.Connect Windows PowerShell on your PC to the Office 365 service:
$LiveCred = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection
2.Grant a user permission to access another user's mailbox:
Add-MailboxPermission <mailbox> -User <user or security group> -AccessRights FullAccess
3.Give Send As permission to users:
Add-RecipientPermission <identity> -AccessRights SendAs -Trustee <user>