He must inform the court of the change of address and the State Disbursement Unit also. If he agrees to a support increase then have a lawyer draft an agreed order ASAP and have the lawyer get it entered for you.
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It is the responsibility of your ex to notify the county if he moves. If they will take the information from you, no harm done. If he still agrees to double his child support payments, get a court order to the effect ASAP but you might wish to find out if there is any chance he should be paying even more than that.
It's his responsibility. Point this out to him. While you're at it, ask him to sign an agreement (have an attorney prepare it) to the double child support figure.
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