You'll want to use Backup/Restore from within ProSeries to backup your client files to a flash drive.   

Use Windows File Explorer and copy the HOMEBASE and COMMON folders to the flash drive as well.

On the new computer, Log into your ProSeries (https://www.intuit.com/sign-in/) account and download/install Proseries on the new computer.  

Once its installed, copy/replace the HOMEBASE and COMMON folders from the flash drive to the new computer (use Windows File Explorer) and then use Backup/Restore within PS to restore the client files to the new computer from the flash drive.