Luckily, this is not possible, as it would be pure spam.
You would need to authorize every single User with the App, request the publish_actions and user_birthday permissions and store an Extended User Token (that is valid for 60 days). You will never get publish_actions approved by Facebook in their review process, because it´s not allowed to autopost. Also, the message must be 100% User generated according to the platform policy.
TL;DR:
- Not possible
- Not allowed
solved Facebook app that automatically writes on fans wall, when some fan have birthday? [closed]