Taking wealth from non-Muslims in treacherous and deceitful ways is haram (impermissible), because deceit is haram in Islam, whether it is done to a Muslim or to a non-Muslim.
What a Muslim is obliged to do is to respect the agreement that exists between him and that country, even if it is a non-Muslim state, because the fact that it is non-Muslim does not mean that it is permissible for him to violate that agreement or betray it and consume its wealth unlawfully.
The brother should have disclosed his work regardless of the debt that he concealed from them.
If Allah guides a Muslim to repent from taking people’s wealth unlawfully, then one of the conditions of this repentance is that he should return to people what is rightfully theirs, even if they are non-Muslims. If there is the fear of humiliation or criminal charges if he returns money to the social services department, then it is permissible for him to look for a suitable way of preserving his dignity whilst also returning money to its rightful owner without embarrassing himself, such as sending the money in the mail or delegating someone to take it to them without mentioning his name or what he did to them. It is not essential for the one who wants to return things to their rightful owners to disclose himself or his identity, because the purpose is to return things to their rightful owners.
If he does not have the whole amount, he may return what he can afford now, and the rest will remain a debt that he owes, which he must return when he is able to.
And Allah knows best.