SynGroups are stored in the articlemarketingrobot.mdb file located in appdata/articlemarketingrobot. That database is backed up by default every time your run AMR. You can toggle this option in tools - options.
Sorry for dumb question but I am partially sighted and cannot always find things easily - so where is the folder appdata/articlemarketingrobot as I want to back it up to a separate disk? With poor eyesight it takes me a long time to build the synonym groups.