Is it possible to get notification when a message from Facebook’s inbox is deleted? Notification can either be email or text message to my cell phone.
Or if there is another way to get notification, suggest it too.
Without creating a custom client there is no programatic way to detect if a message has been deleted. Facebook has no notification or alert which covers message deletion. It does not show on your activity log.
If you link your Facebook account to an email address that your partner has no access to, you can get a notification that a message has been received. This may not, however, contain the full content of said message. You could also achieve this with mail forwarding to another email account.
1) Regularly send messages to yourself using a second account, or (as Facebook doesn't like you creating "dummy accounts") get a friend to send messages. You can then look for these messages.
2) Deny access to Facebook to your partner. This may require you both to resolve any trust issues you may have.
No, it is not possible to get an email or mobile notification when deleting a Facebook message.
Note that deleting a message is a difficult process, one that doesn't happen accidentally. It is possible your partner simply archived the messages -- you can still view these messages, and they will reappear if messaged again by the same individual. (Source)
For more information, see Reading & Deleting Messages from Facebook's Help page.