Can he give charity from his mother's wealth without her permission?

One day I was in the market where I met an elderly man who asked me for some money, but I refused to give him since the money belonged to my mother. I thought that she would suspect something about the missing amount. Was I right in doing so?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad , is His slave and messenger.

There is nothing wrong with what you did. Rather, it is sound behavior since you cannot spend your mother’s money except with her permission. The Messenger of Allaah , said: “It is not permissible to consume any Muslim’s wealth except with his consent.” [At-Tirmithi]. This ruling is applicable if it is a deposit or if your mother entrusted you to deal in a specific transaction. However, if it is a loan, then you may spend it as you like.

Allaah Knows best.