If you created the distribution group as just a distribution group, you cannot use it for security access. You can create a distribution group as a security group instead and that will work.
A distribution group is just a list, not a security group.
I am a little confused about the steps you took. It sounds like you created a dist group and then told exchange to also create a mailbox associated with it. Did you create a separate mailbox with a different name than the distribution group?
When you added users to the “mailbox” do you mean to the distributiuon group you created and then added that dist group to the mailbox?
What a working scenario would look like is this:
Create a dist group (also called a public group) with an email address, create it as a security group.
Create a separate mailbox with a different name.
Add the public group to the mailbox rights of the mailbox. Give exchange 20-30 minutes to replicate and then you should be able to open the mailbox. You can give the group full access to the mailbox in the exchange management console.
Here is a step by step process:
Open Active Directory Users and Computers
Browse to the desired OU
Create a new USER ID. Make sure to give it an Exchange mailbox.
Create the desired SMTP address for that user (i.e. GroupOfPeople@company.com )
Go back to ADUC and browse to your Groups OU (if you have one)
Create a new Security Group and add the desired members
In ADUC go under View and check the Advanced option
Open the USER ID you created previously.
Go to the Exchange Advanced tab and click on the Mailbox Rights button
Add the desired Security Group and make sure that Read Permissions and Full Mailbox Access are checked – hit OK
Go to the Security tab and add the Security Group. Make sure they have Read, Write, Allowed to Authenticate, Receive As and Send As checked. – hit OK
Wait about 5 minutes.
Go into Outlook, Tools, Account Settings, Change, Advanced, Add the USER ID
Repeat this for each person in the Security Group and you will all have access to the mailbox.