Found this on google...
If you are fully blocked in Facebook, both on messages and from their Facebook profile, you won’t be able to find the person you wish to message in Messenger Search or on Facebook Search through your profile.
If you have been blocked only from Messaging after a previous messaging conversation, the next time you try to message or reply to the other persons last message there will be a pop up saying. “Message Not Sent This person isn’t receiving messages from you right now.” You may also get a red circle icon with a red question mark left side of your message. When you click the red icon it will tell you there has been a problem connecting with messenger.
The profile icon in messenger of the person that is blocking you will also no longer show the Facebook Messenger badge, but will only show a grey Facebook Logo, indicating you cannot contact them via their message app, or that they may no longer have F.B Messenger app.
Facebook users that have never activated Facebook Messenger on their mobile device, will have only the grey Facebook Logo on their profile picture that shows up in Messenger.
If you are blocked from contacting the other person via Facebook Messenger, you will not be able to text them, or audio or video call them, you will get a message saying they are not available to you right now.