Taking money to help a son without his mother's knowledge

Hello. A man is very ill and needs expensive treatments; his elderly mother has a lot of money, but she has not been informed that her son is ill so as not to distress her. May the brother who manages the mother's funds give the sick brother money from the mother's assets, claiming that if she knew, it is reasonable to assume that she would give it to him?

Hello and blessings.

It is permitted.

The Shach in siman 358, se'if katan 1, disagrees with Tosafot and Hagahot Ashri, who say that even if it is known with certainty that, were the owner aware, he would agree to the use of his property and consumption of its produce, it is nevertheless forbidden, since we rule that "ye'ush shelo mi-da'at" is not considered ye'ush. The Shach disputes this and distinguishes between a case of ye'ush where a person despairs against his will and our case, where he would willingly agree. The poskim disagree whether we follow the Shach even in a situation where the principal itself is diminished; in such a case there is certainly room to be lenient, since the mother would surely have given to her son.