Oh God! My eyes....
How (Not) To Ask A Question

#!/usr/bin/perl use Net::FTP;
use Archive::Extract;
use File::Listing qw(parse_dir);

$host = ''; $path = '';
$ftp = Net::FTP->new($host, Timeout => 1800) or die "Cannot contact $h
+ost: $!";
$ftp->login('username', 'password') or die "Cannot login ($host):" . $
+ftp->message;
$ftp->cwd($path) or die "Cannot change directory ($host):" . $ftp->mes
+sage;

@Files = $ftp->ls('-lR');
#$ftp->binary();
$ftp->ascii();
foreach $file (parse_dir(\@Files)) {
  my($name, $type, $size, $mtime, $mode) = @$file;
  print "Retrieving $name \n";
  print "File type $type \n";
  if ($type != 'f') {
    print "File name: $name";
    print "File type: $type";
  }
  if ($type eq 'f') {
    $ftp->hash($name,102400);
    $ftp->mput($name, '/data/UC4/outbound/CustomerStatement/*.txt') or
+ warn "Could not get $name, skipped: $!";
    EXTRACT("$name '/data/UC4/outbound/CustomerStatement/*.txt');
  }
}

$ftp->quit or die "Could not close the connection cleanly: $!";

sub EXTRACT {
  my $ae = Archive::Extract->new( archive => @_ );
  my $ok = $ae->extract( to => 'LOCATION' );
}

exit;
[download]

The first thing that is immediately obvious on actually being able to read the post is that you're missing a double-quote on line 24. Is this the exact script that you're running?
Updated
After looking at your script some more, I think you're wanting to do something more like this.

#!/usr/bin/perl

use strict;
use warnings;
use Net::FTP;

my $srcHost = '';
my $dstHost = '';
my $path = '';
my @getFiles = ();
my @putFiles = ();

#connect to your source machine first
my $ftp = Net::FTP->new($srcHost, Timeout => 1800) or die "Cannot cont
+act $srcHost: $!";
$ftp->login('username', 'password') or die "Cannot login ($srcHost):" 
+. $ftp->message;
$ftp->cwd($path) or die "Cannot change directory ($srcHost):" . $ftp->
+message;

#then get the list of all files
@getFiles = $ftp->ls('-lR');
foreach my $file (@getFiles){
  #do whatever it is you're doing to decide if you want the file or no
+t
  if(&SOME_FILE_TEST($file)){
    #get the file and save the name
    if($ftp->get($file)){
      push(@putFiles, $file);
    }else{
      warn $ftp->message;
    }
  }
}
unless($ftp->quit){
  undef $ftp;
  warn "Could not close the connection cleanly: $!";
}

#now you need to connect to the destination server
$ftp = Net::FTP->new($dstHost, Timeout => 1800) or die "Cannot contact
+ $dstHost: $!";
$ftp->login('username', 'password') or die "Cannot login ($dstHost):" 
+. $ftp->message;
$ftp->cwd($path) or die "Cannot change directory ($dstHost):" . $ftp->
+message;

foreach my $file (@putFiles){
  unless($ftp->put($file)){
    warn "Failed to put $file:  " . $ftp->message;
  }
}

$ftp->quit or die "Could not close the connection cleanly: $!";

sub SOME_FILE_TEST{
  #do whatever you want here
  return 1;
}
[download]

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