You can move after submitting the application. However, you're supposed to keep USCIS updated for any address changes (call customer service number).
If you move out of the district where you filed, your application may get delayed while they move your file to the new district office (e.g., National Benefits Center sends it to your old district even though you updated the address months ago, file sits on someone's desk for a few months, you call customer service and initiate an inquiry, file gets forwarded to new district office, gets lost en route, you call customer service and initiate a second inquiry, months later a janitor finds the file in a closet and it gets forwarded to the new district office). It is also possible (but not probable) that USCIS gets the address change right and there is no delay. Good luck.