To preserve all the data, you will have to copy te3 directory inside html directory from your old server to your new server. There are several methods how this can be done, we'll describe just one of them here:
cd into the html directory for the respective domain. te3 directory inside html directory on the old server: tar czf archive.tar.gz te3 archive.tar.gz to your local machine using your favorite FTP client and then upload it (in binary mode) into the public_html folder on the new server. cd into the html for the respective domain. archive.tar.gz using the following command: tar xzf archive.tar.gz te3 directory (including all the sub-directories and files) inside html directory on your new server now. install.php into your public_html/your_TE3_directory/ directory in binary mode. Chmod install.php to 755. http://www.yourdomain.com/your_TE3_directory/install.php and follow the instructions. install.php (recommended), or chmod it to 0.
It is extremely important to test if .htaccess protection is working properly.