The 5th commandment, “Honour your mother
and your father” is considered by the the rabbis to be a Torah precept
that applies both to Jews and non Jews alike. The convert to Judaism is
not obligated to recite kaddish for their non-Jewish parents. Their is
general agreement among the rabbis that those who had converted were not
prohibited from saying kaddish if they wish and, by so doing are fulfilling
the requirement to give due honour to their parents.
Rambam, (Maimonides) with reinforcement
from the Shulchan Aruch1, stated that one who has converted
to Judaism must continue to respect his non-Jewish parents and must be
recite kaddish for them.
There is rabbinic responsa which would
suggest that this would also apply in regard to non-Jewish parents-in-law.
There are, of course, dissenting opinions
also to be found. These would indicate that to do so would not in fact
constitute a transgression.