Can I fast for my deceased grandma?

So my grandma died a week ago, and she meant a lot to me. She was not extremely religious, however she lived a very difficult and oppressed life, which really saddens me. Due to all the hardships she faced in this life, I really really really hope Allah grants her Jannah, and I want to help increase her good deeds. Since she died, I have been reciting the Quran everyday and dedicating it to her. I intend on doing this until I die as well. Also, I fasted yesterday, and prayed that she would get the reward from my fasting. However, my mom said she has never heard of fasting for someone else, and doesn't think I should be doing that. Is she right?