I could solve this problem by removing these 4 lines:
$this->loader->add_action( 'login_form', $this->fbl, 'print_button' );
$this->loader->add_action( 'login_form', $this->fbl, 'add_fb_scripts' );
$this->loader->add_action( 'register_form', $this->fbl, 'print_button' );
$this->loader->add_action( 'register_form', $this->fbl, 'add_fb_scripts' );
From class-facebook-login.php and adding the shortcode [fbl_login_button redirect=”” hide_if_logged=””] where I wanted it. It also helped to set the redirection correctly.
