Edin Kadribasic has posted the latest release of his helpful little patch for anyone needing the client libraries for MySQL on Windows - the version for PHP 4.4.3 and MySQL 5.0.22 libraries.
After the final release of PHP 4.4.3 here are the Windows binaries who need PHP compiled against newer version of MySQL libs.
The archive contains two files. Both of these files should be dropped in your existing php-4.4.3 install folder overwritting php4ts.dll and adding libmysql.dll.
You can download the file directly from here.