I want to write one php script that will copy one particular file from one web server( linux ) to another( linux ).
You could execute rsync in PHP like so.
exec('rsync -ruva --progress /local/file.png user@remote.server.com:/tmp/file.png');
Check here for information on how to setup passwordless ssh for rsync to run.
In php you can use fopen and fgets (see also http://php.net/manual/de/features.remote-files.php)