Are the children of the deceased wife entitled to claim their mother's inheritance, knowing that what the mother owned came from the husband's wealth which he bequeathed to her, and what is the mother's standing before Allah?

If the registration of wealth in the wife's name was not intended as ownership, then it is not considered a gift, nor does it enter into her inheritance, and her children have no right to claim it. For in contracts, intent matters. The children must fear Allah and not claim these assets if they were not truly your wife's property. If you have evidence proving that this wealth is yours, then present it; otherwise, judgment will be based on what is apparent. The wife absolves herself if she clarifies to her children that the assets registered in her name are not truly hers. The sin falls upon the children if they wrongfully take the money, for Allah Almighty says: (And do not consume your properties among yourselves through falsehood) and the Prophet, peace be upon him, said: "If I judge in favor of someone concerning a right belonging to his brother, he should not take anything from it, for I am merely cutting off a piece of Hellfire for him."