Praying on behalf of one’s parent:
It is a Mitzvah for one to pray to God on behalf of his parents, and that God blesses parents with health and a livelihood. So is the custom followed by all Jewry in the Harachamans of Birchas Hamazon. Furthermore, some write that doing so fulfills the biblical command of honoring one’s parents.
 See Kav Hayashar 65; Olas Tamid 30 [Rav Shmuel Hominor]; Darkei Chaim Veshalom 308; Beis Yehuda 8:9; Shaareiy Tziyon 3:8
 Olas Tamid ibid; Darkei Chaim Veshalom ibid