Hi,
Easy Profile is a profiler component. PM is not a features of Easy Profile.

BUT you have different way to do this:
1. Joomla Contact integration
- You can enable the "User - Contact Creator" built-in Joomla plugin. With this when user register the plugin create a contact item linked to this user. In profile view you will see a "Email" button linked to contact card with contact form.
2. You can create your button to send PM with simple HTML module and our Content plugin (docs at https://www.easy-profile.com/docs/26-plugin-content.html, this is available only for paid members).
I think that 3rd party extension have some link to send email to predefined user by a link like: index.php?option=com_pmextension&view=write_mail&user_id={user id displayed}
with {user id displayed} our plugin render the id of displayed user, you can set this module to be visible on profile page
Also you can override profile page template to add this link (you can do this on free version)
3. Based on our main concept "Easy Profile is a profiler component", we have added a PM with conversation on another plugin called "Social Network - Plugin", see a demo here http://socialnetwork.easy-profile.com/ this plugin make Easy Profile as Social Network component