Thanks Patrick for your fast reply. I think the submit succeeds, as it triggers the next State, and the workflow is completed successfully, also the InfoPath form fields data is written normally to the columns of the SharePoint list, ie: although I can see the data in the columns, I can't see it on re-opening the InfoPath form. Regarding the order of the submit and close: actually I tried both: separate actions and separate rules, and in both cases I first submit then close the form. I noticed something, when adding the close action I see this message: "Prompting the user to save the changes during the 'Close the form' action is not supported in Web browser forms", any idea why?
My best guess is that there is a problem with the saving of the form, I don't know how to enable the saving. Or maybe I need to add a "Receive data" data connection, but also I don't know how to make the data appears in the exact fields of the InfoPath. Regarding "check the saved data by opening in notepad and verifying the fields" how can I open my submitted form in a notepad?