Yes, both the Babylonians and Assyrians recorded their conquests, both in monuments and in their annals/chronicles of major events. I discuss those records in the comparison to the Biblical book of 2 Kings in this thread. Of course, that thread is focused on the conquests of Israel/Samaria and Judah specifically, but it links to the primary sources which also refer to the conquests of the Phoenician cities and non-Hebrew peoples of southern Canaan.