Yes, submit your change of address immediately. Although it may not have any consequences, technically you have violated immigration regulations. But have no fear, they will probably just look the other way.
Don't waste your time suing criminals, for one, their activity is not covered by insurance, and two, if they are engaging in criminal activity, they likely judgment-proof. What you could do is make sure to tell the prosecuting attorney to make it a condition of any plea offer to them that you get paid for your losses. You may even be entitled to compensation from the victims' fund. Good luck.
I believe you're omitting crucial information. Did she endorse the check, did she know about your claim? Answering these questions will be important to determine whether she is entitled to a portion of your settlement, which I believe is what you want to know.
More information is needed, but usually with a serious injury such as yours, if you can prove negligence and causation, then there is a possibility for recovery. Contact a personal injury attorney for consultation.