I havn't tested these recently, but you might get a head start with Sockets-File-Upload with Net::EasyTCP and File Transfer via Sockets and Indirect file transfer. Also don't forget netcat , you can google for it's usage.

Just to demonstrate the base simplicity of the concept, here is a rudimentary server & client set

Server

#!/usr/bin/perl -w
use strict;

use IO::Socket::INET;

#--
#-- server.pl
#--
my $server = IO::Socket::INET->new(Listen    => 5,
                                   LocalAddr => 'localhost',
                                   LocalPort => 5050,
                                   Proto     => 'tcp') || die $!;

#-- have we receive the filename from the client yet?
my $file = undef;

while(my $client = $server->accept){

        #--
        #-- in your code, you have while(<$client>){...}
        #-- which is very dangeous because <> will hang if
        #-- client and server use a different newline encoding
        #-- so please avoid using <$client> in your networking code
        #--
        #-- 1024 is also a hack which assume your filename will not
        #-- be longer than 1K.
        #--
        while(sysread($client,$_,1024)){

                #--
                #-- look for a filename before the first newline
                #--
                if(/(.+?)\n(.*)/ && !$file){

                        #--
                        #-- for demo, i will create a filename (sent i
+n by client)
                        #-- appending with .by_server. this helps you
                        #-- to run this demo code without worrying ove
+rwriting
                        #-- the original file in the same machine
                        #--
                        $file = $1 . '.by_server';
                        open(FILE,">$file") || last;
                        print FILE $2;
                }else{
                        print FILE if($file);
                }
        }

        close(FILE) if($file);
        close($client);
        $file = undef;
}

__END__
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Client

#!/usr/bin/perl -w
use strict;

use IO::Socket::INET;

#--
#-- client.pl
#--
my $server = IO::Socket::INET->new(PeerAddr => 'localhost',
                                   PeerPort => 5050,
                                   Proto    => 'tcp') || die $!;

my $file = 'tmp.txt';

#--
#-- send the file name to server.pl
#--
print $server "$file\n";

#--
#-- and then the content
#--
open(FILE,$file) || die $!;
print $server $_ while(<FILE>);
close(FILE);

close($server);

__END__
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