I’m active duty military stationed in NJ but living in PA (with a PA DL). One of the main reasons for moving to PA was so that I could get NFA items. One of the questions that came to me recently when going over some of the threads about how to SBR a rifle was “What happens when I move?” From my understanding is that I have to have my city/state engraved into the firearm. My concern is that even though I’ve been stationed in NJ for 10 years there is a good chance that I’ll be forced to move before I retire in 10 years (especially since I tend to move about every 3 years for some reason anyway). So what are my options or am I screwed?
When you move you must notify ATF of the change in address in writing. The location you move to must allow the type of NFA item you have or it will not be approved. Not all states allow SBRs. As far as the engraving, no further action is required. That only applies to the initial manufacture/application. If your NFA item is stored in another location from where you physically are, it must be secured where no one but you has access. This is different if you have it under a trust or corporation.
All items will be registered under a trust. I’m aware that not all states allow SBR and other NFA items, like I said, I moved from NJ to PA for this reason. 
Thanks for your other info.
Are you a KC-10 boomer? If so, you’re limited in your base selection as long as you keep flying. If you get Travis AFB, CA, then you can say good-bye to the “toys” for a while. However, I’ve known a number of KC-10 guys that managed to homestead.
If you’re in a flying squadron now, stay until they want you to move and then volunteer to go over to the 621st Contingency Response Wing next door. A PCA there will easily buy you at least 3 ~ 4 years additional time of station.
Yes, I’m a KC-10 boom operator. Again, I know what bases I can go to and what my options are in those states. I’ve been on active duty for about 10.5 years and stationed in NJ for 10 years this month. I currently have about 2.5 years left in my non-flying billet and then I should go back to either the 2nd or the 32nd ARS. Due to my current non-flying assignment they will not send me to any of the CRWs since I’d lose my flight pay. I will gladly talk about this offline (outside of this thread), but I’d like to keep responses on track in case anyone has anything else to add to what Firecop already posted. Thanks. 
You will be required to fill out a 5320.20 just like you do when taking it across state lines for classes, shoots, get togethers, etc. You will just express that it will be a permanent move (I believe there is a checkbox for that.)