If this is a true "Shared Mailbox" - that is when you look up the mailbox type it is "Shared Mailbox" than you can't logon directly. You can only access it thru a User Mailbox.
If this is just a user mailbox that is "shared" - then you can logon using that mailbox alias and configured password.
However - in both cases it's not really necessary if they are looking to just interact with people as the "Shared" mailbox. You can grant them the ability to not only access the mailbox thru their account, but also give them send as permission so they can send mail on behalf of the mailbox.
Update
Based on the feedback below - this is not possible via any server or client settings I'm aware of. It is possible to differentiate the UPN (for logon) and the primary email address, so those can be different on a mailbox. However you can't set the mailbox primary email address to the same one that is configured for the Shared Mailbox.
Outside of the provided server setup. The client might possibly be able to leverage VBA so that when a new message is created it will automatically change the "from" address to the shared address.