If you don't have access from server A to server B, I'ld simply use some key appended to the end of the URL, like this:

On server A (using mason):

use Digest::MD5 qw(md5_hex);
my $ip=$r->connection->remote_ip();
my $url="/gotohere/";
my $basekey="somespecialkeyequalinsiteaandsiteb";
my $sid=md5_hex("$ip;;$url;;$basekey");
$url="http://www.siteb.com$url?sid=$sid";
$r->redirect($url);
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In a autohandler on site B:

use Digest::MD5 qw(md5_hex);
my $sid=$ARGS{sid};
my $url=$r->uri();
my $ip=$r->connection->remote_ip();
my $basekey="somespecialkeyequalinsiteaandsiteb";
my $vsid=md5_hex("$ip;;$url;;$basekey");
if ($sid eq $vsid) {
   $m->call_next();
}
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The same can be used in CGI or ModPerl, with small changes, I think.