I looked into it. The back of the Form 4 says that you only have to notify the ATF in writing of the change of address.
From the Form 4...
"Unless currently licensed under the Gun Control Act, the registrant shall notify the NFA Division, Bureau of Alcohol, Tobacco, Firearms and
Explosives, 244 Needy Road, Martinsburg, WV 25405, in writing, of any change to the address in item 2a."
So the best thing to do is merely let them know what your new address is. The instructions don't say if you have to remind them of what you have.
So the letter could read...
"This letter is to inform you that my new address is..."
Unless they ask for it, there is no need to volunteer to them the make, model and serial number of the suppressor.