Is it permissible for a beneficiary of social welfare from a Western country to buy a house and register it solely in the name of his first wife and her children, given that the second wife does not benefit from this welfare? And is it permissible for him to spend on the second wife from this welfare with justice among the wives, or does the first wife have the right to more spending due to her and her children’s right to this welfare?

The husband must be equitable between his wives in all matters, as indicated by the general body of evidence. The Prophet, peace and blessings be upon him, said: "Whoever has two wives and inclines to one more than the other, will come on the Day of Judgment with his side leaning."

Therefore, if the entire aid is given to you in your capacity as the head of the family and its provider, then you have no right to exclusively give any of it to your first wife.

If the aid is distributed – a portion for you, a portion for your first wife, and a portion for your children – then it is not permissible for you to spend anything that has been given to your wife except with her consent.

In that case, there is no objection to purchasing a house with what has been gifted to her and her children, and registering it in her name and the names of her children, because the money is theirs. You do not have the right to dispose of it except with the consent of whoever's consent is considered from them, namely the adult of sound judgment. As for the one who is not of sound judgment, his money may only be disposed of in a way that benefits him and serves his interest.