Wa alaykum salam wa rahmatuLlah,
One may give zakah to his stepmother so long as she meets the requirements that make one eligible to receive zakah. (Hashiyah Qalyubi/Umayrah v. 2, p. 195; Mughni al-Muhtaj v. 3, p. 106)
And Allah knows best.
Shafiifiqh.com Fatwa Dept.