Under the law, a Resident (Conditional or Permanent) you are required to notify USCIS if you move. It is quite easy to do on line, using form AR-11. As far as when you can apply to naturalize, if you are married to a US citizen, then you can apply 3 years after you received your residence, but only if you have been married to the US citizen for 3 years. If you are not married to a US citizen, then 4 years and 9 months after you received your Residence.
Answered on Nov 14th, 2013 at 12:32 PM