How to troubleshoot the Exchange offline address book with Office 365

I was recently working on an issue for a client who is currently in Exchange  hybrid mode with Office 365.  They were updating phone numbers for user accounts in their on-premises Active Directory and noticing that the Outlook offline address book (OAB) was not reflecting these changes even after waiting the requisite 24 to 48 hour period in which changes and updates should be showing.  What we found was an incorrect DNS record for autodiscover.
The autodiscover record in DNS was set to their hybrid server during the time that mailboxes were being migrated to Office 365, and had never been set to “”, which is the correct setting for Office 365.  This was preventing updates to the OAB from downloading to Outlook clients.  Microsoft has a good support article for troubleshooting the OAB in an Office 365 environment located here.  Of particular interest is section 6 on testing the autodiscover service:
“Step 6: Determine whether the autodiscover service is working, and check access to the Offline Address Book
Note: If the Offline Address Book issue wasn’t resolved by using steps 1 through 5, follow this step for validation before you call Support.
Check whether Outlook and the computer can access the Offline Address Book file on the server. This action is typically done by Outlook in the background or when you force a download of the Offline Address Book in Outlook. To do this check, sign in to the Office 365 portal, and then follow these steps:

  1. Start Outlook.
  2. Hold down the CTRL key, right-click the Outlook icon in the notification area on the right side of the taskbar, and then click Test E-mail AutoConfiguration.
  3. Click to clear the Use Guessmart check box, and then click to clear the Secure Guessmart Authentication check box.
  4. Click to select the Use AutoDiscover check box.
  5. Type the email address and password, and then click Test.
  6. On the Results tab, note the path of OAB URL.
  7. Click the XML tab, locate the <OWAUrl> and </OABUrl> tags, and then copy the path that’s displayed between the tags. Paste the path into the address box in Windows Internet Explorer, add /OAB.xml to the end of the path, and then press Enter.The following is an example of what the URL may resemble:

  1. Note the information that’s displayed in the webpage in Internet Explorer. The webpage should contain lots of XML data. The following is an example of the information that should be displayed in Internet Explorer:”

The built-in test for E-mail AutoConfiguration is a great hidden tool within Outlook 2013.  The log file quickly pointed me in the right direction.  Here is what the tool looks like: