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If the children are still under the age of 18 then yes she can take him for child support. The chances of getting back child support.
Her first step is to go to your local Child Support Enforcement Agency and asking for services. This is normally free but if her income is high they may request a 25.00 fee.
They will give her a packet to fill out she can give them his social security number and any other information she has. Fill the packet out and return it. They will get in touch with him and set up a hearing to establish support amounts and then the judge will court order it. At which time they can either garnish his wages or allow him to pay by check (Garnishment is much more common).
They will then send the money to her each month in the form of a check or though a child support debut card.
It is not difficult and they can help her.
She may also be entitled to other support so she may want to consider getting into contact with a lawyer to determine what all she is entitled to.