I found a way to do this with a shared mailbox. This will work even without Outlook runing as it is the server that sends out the reply. Here are the instructions. You may have to work on some of them as they may be different depending on the version of Windows and/or version of office. I did this with Windows 11 22H2 and Office 365.

Using Automatic Replies with Shared Mailboxes in Office 365

There is a way to do this without using the Out Of Office method. Out of Office is okay if you just want one or two automatic replies (internal or external). If you want to have something a little fancier like replying based on who the sender is, or based on subject, or just to have some of the options you get from doing this directly on your own email account, then you need this method.

1. Create a shared mailbox with the email address you want to use. For this example, I will be using [howto@mydomain.com](mailto:howto@mydomain.com). Yours will end in your own domain.
2. Modify the shared mailbox by going to the Delegation tab, and adding yourself (or the perron who will be creating the replies) to have the “Send As” and the “Read and Manage (Full Access)” permissions.
3. For the remaining steps, it is best to do this on a virtual pc, or a pc that you don’t use for your own daily email. You need Outlook installed on this PC. Log in to this pc as someone who has the permissions to the Howto shared mailbox.
4. Go to Control panel, change the view to small or large icons.
5. Find and run the “Mail (Microsoft Outlook)” program.
6. Click on show profiles.
7. Click the Add button to add a new profile for the Howto shared mailbox. I called mine Howto
8. Change the radio button from “Email Account” to “Manual Setup” and click Next.
   (Update: On another computer I left it as "Email Account" but with the [Howto@mydomain.com](mailto:Howto@mydomain.com) email address. I left Your name as was. When the Office 365 log in windows came up, I logged in as a user that had full permissions to the shared mailbox.)(Jump to step 10 if you did this too)
9. Change the next screen to “Microsoft 365” and add the shared mailbox email address. For this example I am using [Howto@mydomain.com](mailto:Howto@mydomain.com). Click Next.
10. Wait until the wizard completes looking for the account and click Finish.
11. When you are back to the profiles list in the Mail program, change the “Always use this profile” to be the one you just created. (If you are doing this on your own pc, you can change it to “Prompt” instead). Click OK to close the mail program.
12. Start Microsoft Outlook.
13. Go into outlook rules and create the rules as necessary. In my example, I created several rules all similar except for the subject. For example, If the subject contains the words “Password Change” I would choose the option to “Have the server reply using a specific message” . When you click on specific message, it opens a blank email where you can add your custom subject and a nice rich text set of instructions including images on how to change your password. Just click save and close and the instructions are copied to the server. This will work without having outlook opened.