To summarize the above: No, it's not okay.
As trustee, he only has dominion over what was transferred to the trust prior to death. His POA became void with his mother's death. The funds still held in his mother's name at the time of death were subject to the probate process and the control of a court appointed personal representative.
He needs to put the money back...
_________________________
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.