Yes, submit an AR-11. You can do it online www.uscis.gov
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Will your mail find its way "one floor down"? What if you get an important notice from the immigration services?
The statutes specify that aliens must notify the government of permanent changes of address. Failing to comply with this requirement is a basis for deportation from the US. If the government wants an alien out of the US, the government will throw this charge in with all the other charges.
Most persons can file the AR-11 online for free at www.uscis.gov . Filing the form takes less than five minutes if you have the information ready. Why would you want to give the government a reason to deport you?