If you have this ‘unique identifier’ stored in a field on your form then you can run a ‘connect’ action as the users load a new instance of the form to be able to advise a form already exists and could then populate the new instance with this data, but this wouldn’t help you in terms of ‘only one stored form’ of course.
There could be a few ways to try to cover this. One could be that when a user submits the form the first time, you send them a ‘notify’ and within the email present them a link to THEIR form, and ask them to ‘bookmark’ it perhaps for future use
If they do load a ‘new form instance’ you could run a connect action as above to then present a message to the user to tell them there is an existing form already and to refer to the email they were sent and then not allow them to enter in to this new form, and if they hadn’t ‘saved’ that, give them instructions on who to contact (ie you perhaps) so you can find the details they need (ie the link to their form).
You could even look to store the ‘link to form instance’ on the form as they first submit it, and if the ‘connect’ action shows they have a form instance already return that link to a field on the form for them to copy/paste into their browser