I had my form printed out ready to go, and then the office closed. Hopefully I remember once the office re-opens.
I see to remember that I need to take my kids as well, rather than just their paperwork, so hopefully it is quick here as well.

I didn't know I had to inform the SSA when I naturalized in 2006. It became an issue in 2011 when my daughter was applying for federal student loans. She indicated on the FAFSA application that she was a US citizen (because she acquired US citizenship through my wife and I becoming US citizens). However, she received a letter from the Dept. of Education stating that her US citizenship could not be verified by the SSA. That's when we had to go in to the local SSA office and have our records updated. We received new SSN cards in the mail and my other kids had no issue with student loans after that.