In Exchange Server 2013 there are multiple methods you can use for granting Send As permissions for a mailbox.
Send As permissions can be granted using the Exchange admin center. Navigate to Recipients, then choose the type of recipient you want to grant Send As right for (in this example I am using a shared mailbox called “Help Desk”). Click the Edit button to open the properties of the mailbox.
Select Mailbox Delegation, then click the + button for the Send As permissions and choose who you are granting the permissions to. Click Add then OK, and then Save to complete the task.
Note: You can add a user or group here. To use a group to grant Send As permissions, which may be easier in the long run, the group simply needs to be a Universal Security group. It does not need to be mail-enabled. However you will need to use PowerShell to configure the permissions when adding a group.
To grant Send As permissions using PowerShell we use the Add-AdPermission cmdlet. Using PowerShell allows either a user or Universal Security group to be given Send As permissions.
[PS] C:\>Get-Mailbox "Help Desk" | Add-ADPermission -User "Help Desk Team" -ExtendedRights "Send As"
Identity User Deny Inherited
-------- ---- ---- ---------
exchange2013demo.... E2013DEMOHelp De... False False
Remember if you're setting up a group for Send As permissions, new members of that group will need to log off and back on again before they can send as the mailbox.