Backup your old site and make sure that you have a working backup.
Install the latest version of jNews on your Joomla 1.5 website. Please contact our support to obtain the latest package.
Copy the folder media/com_jNews from your old website to your new website
In your Joomla 1.5 site, export jNews tables using phpMyAdmin then import them on your Joomla 2.5 website.
Make sure to change your table prefix to the one you used on your new website. Open your exported database using textwrangler or notepad and replace the "prefix_jnews" to your new prefix and then import the file on your Joomla 2.5 website.