Honor your Father and Mother (Part 2): Honoring Stepparents
What is the nature of the obligation of kibud av v'em as it relates to one's stepmother or stepfather? The Gemara learns that the obligation to honoring a stepparent is an extension of honoring one's biological parent. Even though this wouldn't apply after one's parent has passed, it still falls into what the Shulchan Aruch calls a "דבר הגון". (based on the command Rebbe Yehudah HaNasi gave his sons as recorded in Masechet Ketubot. It is important to show gratitude to someone for everything they did for one's biological parent.
Provided courtesy of rabbisilber.com