Because this plugin is integrated with wordpress comments, it is very easy to export and import using the following method. This method is used all the time for exporting and importing wordpress data.
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1. Download this plugin. WordPress Importer
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2. After this plugin is installed, under your new website go to Tools -> Import to import the exported data from your old site.
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3. If you don't know how to export the data from your old site, you go to tools -> Export. (Make sure you have All Content selected to export.