Generally host will purge the raw weblog after it has been generated by various webstats program (analog/awstats/webalizer), there is an option to enable rawlog backup in cpanel hosting account but that will only start backup rawlogs to your hosting account from the time you enable it.
Various webstats program data files are stored in /home/yourusername/tmp/ , if you are transferring to an identical system, you can try upload them back to the same location to see if it works, though no guarantee it will work (the log file may not be in sync when it start generating again)
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