You have not shown how you generate the value of $viewState, which is pertinent here. However it won't make any difference since you define the value of $param in single quotes, meaning $viewState won't be interpolated anyway.

You also are using the most inconvenient way of building and making your request. Consider using at least HTTP::Request::Common, if not something simpler such as HTTP::Tiny.

Sometimes sites are just so anti-scraping that you can't get there with LWP. This seems to be one of them. I don't think your problem is your proxy. I couldn't retrieve the page via LWP either. I am able to get search results using cURL with the same args: try running this from your command line and see what you get:

curl -L 'https://patentscope.wipo.int/search/en/search.jsf' -H 'Host: 
+patentscope.wipo.int' -H 'User-Agent: Mozilla/5.0 (Macintosh; Intel M
+ac OS X 10.11; rv:53.0) Gecko/20100101 Firefox/53.0' -H 'Accept: text
+/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8' -H 'Acce
+pt-Language: en-US,en;q=0.5' --compressed -H 'Referer: https://patent
+scope.wipo.int/search/en/search.jsf' -H 'Content-Type: application/x-
+www-form-urlencoded' -H 'Cookie: JSESSIONID=CD31D066DF8710F9FE9B5C9C5
+397A977.wapp1nC' -H 'Connection: keep-alive' -H 'Upgrade-Insecure-Req
+uests: 1' --data 'simpleSearchSearchForm=simpleSearchSearchForm&simpl
+eSearchSearchForm%3Aj_idt379=FP&simpleSearchSearchForm%3AfpSearch=bru
+shless+motor&simpleSearchSearchForm%3AcommandSimpleFPSearch=Search&si
+mpleSearchSearchForm%3Aj_idt447=workaround&javax.faces.ViewState=7923
+733300114075152%3A8489940171963107341' | grep 'Tokyo Parts'
[download]

I don't know how long the tokens will be good for. That command will probably stop working after some time.

You may have to move up to WWW::Mechanize (which handles cookies) or even Selenium::Remote::Driver (which handles JavaScript).

Hope this helps!

update:: add mention of Mech, thanks Corion...

Please provide an SSCCE. It is impossible to help with what you have shown.

You should be able to provide a script of < 20 lines that attempts the POST request. Remove all the other code in your program and reduce to just the HTTP transaction. Then, post that here if it doesn't do what you want.

Also, before you even do that, please read Posting on PerlMonks.

ok edited, i don't know if the posted code above was sufficient, so just in addition i post the full code here

#!d:\perl\bin\perl.exe 
use warnings;
use strict;

use CGI qw(:standard);
use CGI::Carp 'fatalsToBrowser';
use LWP;
use HTTP::Request::Common;
use HTTP::Cookies;
use HTTP::Headers;
use LWP::Debug qw(+);
use URI::Escape qw(uri_escape_utf8 uri_escape uri_unescape); 
use Encode;

print "Content-type:text/html;charset=UTF-8\n\n" ;
our $page;
my $jsessionID;
my $viewState;
sub extractLinks(){
$page =~ s/\"\/search(\/.[^ ]+)+\"/https:\/\/patentscope\.wipo\.int\/s
+earch$1\" /g;
}


sub extractJSessionID(){
my $jsessionID="";

if($page =~ /(jsessionid=[A-Z0-9]*\.wapp[0-9]n[A-Z])/si){$jsessionID =
+ $1;}
return $jsessionID;
}

sub extractViewStateID(){
my $ViewState="";
if($page =~ /javax.faces.ViewState:0\" value=\"(-?[0-9:]*)/si){

$ViewState = "javax.faces.ViewState=".$1;}
$ViewState = join( "%3A", split(":", $ViewState) );
return $ViewState;

}
my $proxy = 'http://localhost:5865'; 

my $ua = new LWP::UserAgent(keep_alive => 0, ssl_opts => { verify_host
+name => 0 });    
$ua->proxy(['https', 'http', 'ftp'], $proxy);
$ENV{HTTPS_PROXY} = $proxy;    
$ENV{'PERL_LWP_SSL_CA_PATH'} = "D:\\CA_certs\\input\\certs";    
my $cookie_jar = new HTTP::Cookies();
$ua->cookie_jar($cookie_jar); 
$ua->agent('Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Trident
+/5.0)');

#download init page for extracting jsession id
my $response = $ua->get("https://patentscope.wipo.int/search/en/search
+.jsf");
die "Couldn't get $url", $response->status_line unless $response->is_s
+uccess;
print $response->status_line;
$page = $response -> decoded_content; 

extractLinks();
$jsessionID = extractJSessionID();
$viewState = extractViewStateID();
print $page;

my $param ='simpleSearchSearchForm=simpleSearchSearchForm&simpleSearch
+SearchForm%3Aj_idt379=ALLTXT&simpleSearchSearchForm%3AfpSearch=brushl
+ess+motor&simpleSearchSearchForm%3AcommandSimpleFPSearch=Search&simpl
+eSearchSearchForm%3Aj_idt447=workaround&$viewState';

#--------- problem part :
my $request = HTTP::Request->new('POST', 'https://patentscope.wipo.int
+/search/en/search.jsf');
$request->header('Content-Type' => 'application/x-www-form-urlencoded'
+);
$request->header('Referer' => "https://patentscope.wipo.int/search/en/
+search.jsf");
$request->header('Accept' => 'text/html,application/xhtml+xml,applicat
+ion/xml;q=0.9,*/*;q=0.8'); 
$request->header('Connection' => 'keep-alive'); 
$request->header('Cookie' => uc $jsessionID.'\; ABIW=balancer.cms41\; 
+wipo_language=en\; BSWA=balancer.bswa2'); 
$request->content($param);

$response = $ua->request($request);
$page = $response->decoded_content();

print $page;
[download]

my $proxy = 'http://localhost:5865';

This line makes me think that we still don't have enough information to help you. What kind of proxy are you running on localhost, and why?