I don't think so ,,there is no rule for that,..... .However just for their reference as you no longer working with the previous company you can send your new offer letter to update to your file....
Yes AOR DOES specifically say if employment changed they do need to know. An offer letter is not required (this isn’t an FSW application). If you have obtained the 12 month requirement already then a letter from your new employer wouldn’t be necessary!. So just due diligence with the update of the address is fine!