is there any way I can grant the user access to edit the form after he submitted?
Hey, Mariona!
Check this step-by-step tutorial that can be your starting point https://support.wix.com/en/article/corvid-tutorial-building-your-own-members-area
E.g. You can display all the information your users submitted on their personal (dynamic) page and let them change/update it.
Here is also an article that shows how to work with the dataset modes and collection permissions https://support.wix.com/en/article/working-with-dataset-modes-and-collection-permissions