Q. May a convert to Judaism say Kaddish for their non-Jewish parent?
A. Kaddish is not a prayer for the dead but a praise of God, whose will rules all things, both life and death. Having become a Jew, a convert will naturally want to use Jewish idiom, terminology and practice, including Kaddish, on every appropriate occasion. So is the death of a non-Jewish parent an appropriate occasion in this sense?
Rabbi Aharon Walkin discusses this question in his collection of responsa, Z’kan Aharon, vol. 2, no. 87, and concludes that a convert may (and possibly must) say Kaddish in these circumstances. Maurice Lamm, in his Jewish Way in Death and Mourning, pp. 82-83), points out other options such as reading a Psalm or studying a portion of Torah in memory of the deceased, but says the decision to do this or recite Kaddish rests with the bereaved.