LWP will support https URLs if the LWP::Protocol::https module is installed. 

##</code><code>##

 can't connect to moz.com:443, the given host is not known at D:/Strawberry_Perl/perl/vendor/lib/LWP/Pr
otocol/http.pm line 46. 
##</code><code>##

#!d:\Strawberry_Perl\perl\bin\perl.exe 

use strict;
use warnings;

use LWP::Protocol;
use LWP::UserAgent;
use Mozilla::CA;
use CGI qw(:standard);
use CGI::Carp 'fatalsToBrowser';
#use lib 'd:\\Strawberry_Perl\\perl\\vendor\\lib\\LWP\\Protocol\\'; #another attempt which failed
#use https;
my $q= new CGI;
print $q->header;
my $B = new LWP::UserAgent (keep_alive => 1, agent => 'Mozilla/5.0', cookie_jar =>{});

my $proxy = 'http://localhost:5800'; 
my $Skript = "http:\/\/$ENV{SERVER_NAME}$ENV{SCRIPT_NAME}";
my $Server = "http:\/\/$ENV{SERVER_NAME}";

$B->proxy('http', $proxy);

$ENV{HTTPS_PROXY} = $proxy;	
$ENV{'PERL_LWP_SSL_CA_PATH'} = "D:\\cert\\input\\certs";	

$B->ssl_opts( SSL_ca_file => Mozilla::CA::SSL_ca_file() );
$B->ssl_opts( verify_hostname => 0 );
my $GET = $B->get('https://moz.com')->content;
print $GET;