“FEP Contact Form” is not maintained. Do not use that plugin.
You can use
[fep_shortcode_new_message_form to="ADMIN_NICENAME"] (change ADMIN_NICENAME) shortcode in any page/post. It will show a form. filling that will send message directly to that admin. You can also use same shortcode to send message to user (change ADMIN_NICENAME according, dynamically also you can fill this, see https://www.shamimsplugins.com/docs/front-end-pm/shortcode/fep_shortcode_new_message_form/ for details).
As your screenshots, you are using custom form. If you satisfy with above shortcode form, that will be good otherwise you have to make custom changes.