My mother receives a pension benefit( T4A) from her deceased spouse. Does she claim this on her income tax?

Yes, the T4A should be issued in her name and have her SIN on it. This is claimed on her tax return for any benefits she received after her spouse's passing.

Any benefits received prior to the spouse's passing will be reported on a T4A as well, but should have their SIN on it, and possibly say "Estate of".