As Kanji suggests, use Net::SMTP. I used the following code and it worked for the three messages I had in my pop3 account but I haven't extensively tested it:

# ...

use Net::SMTP;

my $smtp = Net::SMTP->new(Debug   => 1,
                          # other stuff
);

# ...

for $msg_id (keys(%$Messages)) {
    print "Retrieving Msg: $msg_id\n";
    my $MsgContent = $pop3->get($msg_id);
    # Here's where I'd like to forward it on..
    $smtp->mail($resentby);
    $smtp->to($target);
    $smtp->data();
    for (@$MsgContent) {
        $smtp->datasend($_);
    }
    $smtp->dataend();
}
$smtp->quit;
[download]

The debug mode will help pinpoint problems. If you get a "broken pipe" message, then one of your supplied arguments ($smtp->mail or $smtp->to) is most likely the culprit.

--Jim