Once someone has left the organization, and their Gmail account is disabled, out-of-office messages will cease to work.  If a manager or colleague is continuing to receive forwarded emails from their account, they are able to set up an auto-reply on behalf of the departing employee.

1. Enable "Templates" in Gmail

Open up your email, click the 'gear' icon in the top right, and select See all settings.

Go to Advanced and make sure that “Templates” is enabled.  If it isn’t, enable it and click “Save Changes”.  This will allow you to create Auto-Reply emails.

2. Write out whatever you'd like the out-of-office message to say.

Back in Gmail, compose a new message and write out what you would like the auto-reply to say.  Then click the "three dots" in the bottom right corner of the message editor, and save it as a template.

Note: If you just enabled Templates in your settings, you may not see this option right away.  Wait a few minutes, and then refresh the page and try composing the message again.

3. Create the auto-reply filter.

Go back into your Gmail settings (gear icon in the top right.)  Then select the Filters and Blocked Addresses tab.  Click on the option that says Create a new filter.

Type in the email address of the departing employee in the "To" field.  Then click Create filter.

Then check the box where it says Send Template, and click Create filter to confirm.

Now whenever an incoming message is forwarded to you, the sender will receive back whatever email you wrote up in Step #2, notifying them that the employee has left the organization.  If you want to turn off this auto-reply 30/60/90 days after the employee has left, you can do so by going back into your "Filters and Blocked Addresses" and deleting the filter.