Jewish Mourning as a Convert

An individual who has converted to Judaism will likely have close relatives who are not Jewish. The individual may choose to observe shiva to honor the death of a close non-Jewish relative although he or she bears no formal responsibilities to observe shiva or other customs of Jewish mourning. While the observances are optional, it is recommended that the individual who has converted to Judaism observe shiva and other Jewish mourning traditions as part of his or her mourning process. If a convert decides to commemorate the life and death of the non-Jewish relative by observing shiva, he or she can choose to receive shiva calls. However, because of the possibility of a slightly modified mourning period, the convert may wish to inform callers that the deceased was not of the Jewish faith.  

Suggested Books:
A Time to Mourn, A Time to Comfort by Ron Wolfson 
When A Jew Dies: The Ethnography of a Bereaved Son by Samuel C Heilman