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<ul>
<li><strong>site_user</strong></li>
<ul>
...
</ul>
<li><strong>calls_waiting_warning_low</strong></li>
<ul>

if ( $form_dump =~ m{(<li>)(.*?)(</li>)}s ) {
    my $inside_li = $2;
    print $fh "Value of \$inside_li: $inside_li \n";
}