Read the back of your approved Form 4. It states to notify the NFA Branch (BATFE) in writing of any address change in 2a of the form. That is all you have to do. No need to fill out any type of forms or get approval. This applies to in state or movement to another state.
This topic is very miss-understood and people confuse it with interstate movement. The only time approval is needed (just state to state) is when you temporarily move a MG, SBR, SBS or DD. Then you must file a form and get approval. Don't need to do this for cans as long as they are legal in that state to use. Any movement inside the state is ok and you don't have to do anything.