Thanks for your question.
She should really have specific contact details for the UKBA on the documentation/correspondence sent to her by the UKBA referring her to ways in which she can update any change in circumstances. I would tell her to look for this, failing that she can contact them in ways described on the following page but she will probably be passed on to the relevant department:-
It will be for the UKBA to decide whether or not to deport him, but following a recent ruling if he is the father of a UK citizen then he will be at liberty to obtain further leave to remain on the basis of this parentage (if he takes specific legal advice, which I presume he would do when faced with potential deportation proceedings).
If he will not accept service of the divorce petition then she can have them served on him by a professional process server that she can instruct privately. The server will then swear an affidavit stating he received the papers and then the divorce can proceed. The quickest divorces usually take around 4-5 months.
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