Based on this website, http://johnpierceesq.com/?p=553
It states the following
"I Am Moving In-State
The good news is that if you are moving in-state then there is no legal requirement that you notify the ATF of your new address. However, up until June of 2013, it was requested that NFA owners send a letter to the ATF when moving in-state so that the NFRTR (registry) could be kept up to date.
Since June of 2013, the ATF has returned such letters with a note that they are no longer accepting address changes in the form of letters and requesting that those wishing to report a new in-state address submit a Form 5320.20.
In summary you have no legal duty to notify the ATF of an in-state change of address. If you wish to do so, you should use a Form 5320.20."
It states the following
"I Am Moving In-State
The good news is that if you are moving in-state then there is no legal requirement that you notify the ATF of your new address. However, up until June of 2013, it was requested that NFA owners send a letter to the ATF when moving in-state so that the NFRTR (registry) could be kept up to date.
Since June of 2013, the ATF has returned such letters with a note that they are no longer accepting address changes in the form of letters and requesting that those wishing to report a new in-state address submit a Form 5320.20.
In summary you have no legal duty to notify the ATF of an in-state change of address. If you wish to do so, you should use a Form 5320.20."