It seems that error is coming because of the debug being true ??
The ajax is returning
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<b>Notice</b>: Undefined index: user_pass in <b>/var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/user.php</b> on line <b>1827</b><br />
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<b>Warning</b>: Cannot modify header information - headers already sent by (output started at /var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/user.php:1827) in <b>/var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/pluggable.php</b> on line <b>925</b><br />
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<b>Warning</b>: Cannot modify header information - headers already sent by (output started at /var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/user.php:1827) in <b>/var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/pluggable.php</b> on line <b>926</b><br />
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<b>Warning</b>: Cannot modify header information - headers already sent by (output started at /var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/user.php:1827) in <b>/var/www/vhosts/9281/domains/android.info.md/public_html/wp-includes/pluggable.php</b> on line <b>927</b><br />
{"success":4}
which makes the script break. I will fix it and release an update soon ( and also check the registration page)
If you want to manually solve it simple change in line 128 in class-facebook-login-public.php the $user variable to the following:
$user = apply_filters( 'fbl/user_data_login', array(
'username' => $_POST['fb_response']['id'],
'user_login' => $_POST['fb_response']['id'],
'first_name' => $_POST['fb_response']['first_name'],
'last_name' => $_POST['fb_response']['last_name'],
'user_email' => $_POST['fb_response']['email'],
'user_url' => $_POST['fb_response']['link'],
'user_pass' => wp_generate_password(),
));