is there any script that detects fb user profile link

hi there. i would like to ask is there any script that silently detects Facebook profile link of any user who clicks on the button on specific site?
I am gonna give an example so that it would be more understandable what I wana ask.

so, let's imagine that there is a site (detect.com) and there is a user (Franklin). so I would like to know is there any script that detects (without any warnings) Franklin's fb profile link when Franklin click on a button on the detect.com.

pls let me know if you found anything for it