You just need send a letter to TSC to notify the change of your address,and explain the reason of moving,it's enough.If the USCIS thinks that it's necessary,they'll require you to provide more detail.
By the way, you also should complete an AR-11 form & send to the Address Change Register Service of USCIS in London ,KY, you may get related information on the web site followed : www.uscis.gov
God blessyou.