# In cPanel PHPMyAdmin export the database and download the export.

# Upload the export to the Plesk Server.

# Use your favorite editor to strip the database header from the export file.
# This will also allow you to upload the database under a different name.

##############################################
# Example of header

--
-- Database: `database_name`
--
CREATE DATABASE `database_name` DEFAULT CHARACTER SET latin1 COLLATE latin1_swedish_ci;
USE `database_name`;

-- --------------------------------------------------------

##############################################

# In Plesk create a blank MySQL database and MySQL username

mysql -uadmin -p`cat /etc/psa/.psa.shadow` database_name < /path/to/where/you/uploaded/the/export.php