What have you tried? The following works for me:

use strict;
use warnings;

open(my $fh_in, '<:raw:encoding(utf16le)', 'src.txt')
   or die("Unable to open src.txt: $!\n");

open(my $fh_out, '>:raw:encoding(utf16le)', 'dst.txt')
   or die("Unable to create file.txt: $!\n");

while (<$fh_in>) {
   if (/[\x{706B}\x{6C34}]/) {
      print("Found one at line $.!\n");
   }

   print $fh_out $_;
}
[download]

The :raw prevents the CRLF->LF conversion when reading and the LF->CRLF when writting. The conversion only works with single-byte, ASCII-based (i.e. LF=0xA, CR=0xD) encodings.

Use :raw:encoding(utf16le) if the file was saved using encoding "Unicode"
Use :raw:encoding(utf16be) if the file was saved using encoding "Unicode big endian"
Use :raw:utf8 if the file was saved using encoding "UTF-8"

Update: Added example regexp to code.