system
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Below is the directory path to the “approvedsenders” (white listed) file. I would imagine the black listed file is in the same location but just called “notapprovedsenders” or something like that. I don’t know for sure because I don’t have any black listed senders yet 
c:\ProgramData\AVAST Software\Avast\Spamconf\approvedsenders
Note: In W7 the ProgramData folder is hidden by default. So you have to un-hide it verify the path I gave you.
You can just backup the “approvedsenders” folder using any of a number of backup utilities. I prefer Sync Breeze which actually copies file in tact and does not condense them. I am not sure but I don’t believe there is an option to backup the lists in using avast!
You can open the “approvedsenders” file to read what is in it by using Notepad, Wordpad or I imagine any software that reads *.txt files