I noticed that the delete message functionality does not work for both users and admin in Front end pm pro. When you select a message or messages and choose delete from the bulk action,nothing happens,the message remains.
I have tested with my test server and it is working here. That means something in your website preventing it to function.
Can you create a test user account in your website for me so that i can access your website and test there?
If yes, send credentials using https://www.shamimsplugins.com/sensitive-information/