As of right now, there is no built-in solution to handle this scenario. It does exist as a feature request, but I cannot elaborate on when/if it will be released. I highly recommend submitting your feedback on the issue if it is a feature you are interested in. I would be happy to do so on your behalf, using the email linked to your profile here.
There is some good news. There is currently a way to asynchronously accomplish this feature through the logs. It requires polling the logs for password changes and sending the user an email when the event occurs in our logs. I would be happy to expand on this idea if you would like.
Let me know if this helps.