Please note: For precision, I’m using the terms from the Google+ API.
As far as I can tell, once you’ve attached an article to a Google+ activity, you can’t change it. You can delete the article from the activity, but once it’s gone, you can’t edit the activity again and attach an article (even the same one). Am I wrong? Is there a workaround?
Currently the API is read-only and the G+ UI does not provide any mechanism for adding an attachment to an existing activity. If the API gets write permissions this may change however.