Is it permissible for them to register what the father owns in one of the sons’ names because their father’s wife wants to do that for herself?

There is no guarantee for the rights of your father’s wife if you register his property in the name of one of your brothers; in fact there is no guarantee for the rights of the other siblings if the property is registered in the name of only one, as you want to do in this case. It is possible that this brother may take over the entire estate on the basis of this registration that you are asking for. In fact there have been many cases like this. Two wrongs do not make a right. 

Just as you have rights with regard to your father’s property that you fear for, the wife also has rights with regard to her husband’s property that she fears for. Just as you fear that she may take over your father’s property, she fears the same thing from you. 

The reality is that this solution offers no guarantees to anyone and it cannot be allowed. 

But if you really fear the possibility of undue influence for your father and his condition does not let him distinguish between what is right and what is wrong, then the Islamically prescribed way of dealing with that is to get a court injunction that will prevent the carrying out of any of his instructions given during the period when he was incapacitated and there was the possibility of tampering or undue influence. 

However we are aware that there are far-reaching social difficulties that may stand in the way of this solution, and there may also be legal difficulties in your country, so you can convince your father to divide his property now among all his heirs who are still alive and transfer ownership to them at the time when it is divided. 

In this manner each party will be protected against tampering from the others. 

And Allah knows best.