It might seem a strange thing to want to do seeing as how distribution groups are traditionally used only for internal email distribution, but many organizations find that a distribution group is preferable to a shared mailbox for some applications. In order to allow a person or group to send email using the address of a distribution group, you need to grant Send As permissions on the distro group. There are two ways to do that:

1. Using the Exchange Management Shell:

Add-ADPermission -Identity “<GroupName>” -User <UserName> -ExtendedRights Send-As

Where <GroupName> is the name of the group and <UserName> is the username, alias, or upn of the user or group to whom you want to grant permissions.  Be sure to use quotes around the group and user names if they contain spaces. If you need to remove Send As permissions, you can use Remove-ADPermission with all the same options.

2. Using Active Directory Users & Computers:
►Open the security tab of the distribution group properties in ADUC. (If you don’t see the Security tab, click on the View menu in ADUC and select “Advanced Features”.)
►Click on the Advanced button to open the Advanced Security Settings.
►Click the Add button.
►Type the name of the user or group to whom you want to grant Send-As permissions. If you want to allow all the members of the distribution group to use the group’s address, you can type the group’s own name here.
►Click the Check Names button to verify you have the right name and then click OK or press Enter.
►Scroll to the bottom of the permissions list and check the Allow box next to Send As, then click OK to exit all the properties windows.

If the permission change doesn’t take effect immediately, there are two things that might be going on.
1. Exchange might have cached some information about the group’s permissions. You can wait a few hours or you can force the change to happen more quickly, by restarting the Microsoft Exchange Information Store service on the mailbox server. If you restart IS, be aware that you will kick any active users out of their mailboxes.
2. Make sure that your distribution group isn’t hidden from the Global Address List. I wish that didn’t matter, but it does.

(Did you notice how much faster the PowerShell method is? GUI methods are usually easier to remember, but PS methods are frequently faster. Where Exchange is concerned, they are also usually more powerful too.)