Open LibreOffice.
In theory simply using File > Open from there should work but I'd rather have the 'Writer' part of LibreOffice on screen first. So click on 'Create Writer Document'.
Then go to File > Open and navigate to the location of passwords.abw, double-clicking on it when you get there.
If it opens, then go to File > Save As and choose a suitable file type from. (If you want to then try opening the file you've saved in Abiword, I suggest trying 'Word 97-2003 (*.doc)' or possibly either 'Text (*.txt)' or 'Rich Text (*.rtf). It might be best to give the file a slightly different name (e.g. 'passwords2') so you can easily tell which file is which.
If passwords.abw won't open in LibreOffice Writer, you might be stuck! All I can then suggest is to try opening it in Notepad or Wordpad. (They're both available from your Start menu, under 'Windows Accessories'). If you can get to a valid document via one of those programs, you can then resave it, as 'passwords2', into one of the formats I've mentioned above.