Sending message to admin: You can achieve that is 2 ways
1. Set 0 to Front End PM PRO > Settings > Recipient > Max recipients
2. Follow https://www.shamimsplugins.com/docs/front-end-pm-pro/getting-started-2/role-to-role-block/

As you are setting only one admin, so “To” field will be hidden and all message will be delivered to that admin.

If you want to send message from user page you can use https://www.shamimsplugins.com/docs/front-end-pm/shortcode/fep_shortcode_new_message_form/ shortcode. In “to” you can use your admin nicename, so that message will be delivered to that admin.