How do you know when the NOA1 or 2 has been processed before the hardcopy arrives?

With the NOA1 you know once the check has been cashed.
Once your Fiance gets the NOA1 in the mail there will be a casenumber on the hardcopy.
With this number you can create a portfilo under www.USCIS.gov ,everytime they do something with your case the date will be changed. This is also known as a touch on here.
This will let you know that you got Approved before the hardcopy.

Thanks!

and for your NOA1: if you sent a check, you can get the casenumber from the back of you cashed check aswell. the website (uscis) will inform you on your NOA1 (normally) faster than the hardcopy.

good luck to you!!