It is forbidden to extend the greeting of "Shalom" to a mourner within twelve months of the passing of his or her father or mother, Heaven forbid. A person who has recently suffered such a loss is not in a position to experience "Shalom," and this greeting is thus inappropriate during this period. A mourner is allowed to extend such a greeting to others; the prohibition applies only to others greeting a mourner with the word "Shalom." It is permissible to extend other kinds of greetings to a mourner, such as "good morning," "good health," and the like. The Sages enacted this prohibition only with regard to the specific greeting of "Shalom." With regard to the common greeting of "Shabbat Shalom" on Shabbat, the Shulhan Aruch, in the laws of mourning, records a custom (based on the Talmud Yerushalmi) to allow extending the greeting of "Shabbat Shalom" to mourners on Shabbat, and this is, indeed, the accepted practice. It is also permissible to extend to a mourner the greeting of "Shalom Alechem" that is customarily exchanged after Birkat Ha'lebana. The reason for this greeting is that since we recite several verses about the downfall of our enemies ("Tipol Alehem Emata Va'fahad…"), we greet one another with "Shalom Alechem" to make it clear that we did not have one another in mind when we expressed our hopes for our enemies' demise. Thus, this greeting is intended not as a friendly gesture, but rather to avoid possible misunderstandings and ill-will, and it is therefore permissible to extend this greeting to a mourner. Furthermore, this greeting is formulated in the plural form – "Alechem" – and thus refers to the entire congregation, and not only to the particular individual that one addresses, and for this reason, too, one may extend this greeting to a mourner. It is forbidden to give a mourner a gift throughout the twelve-month period after a parent's passing. There is no greater "friendly greeting" than a gift, and one therefore may not give a gift to a mourner within twelve months after the passing of his or her parent. This discussion applies only to one observing Abelut (mourning) over a father or mother, Heaven forbid. In the case of one who lost another family member, Heaven forbid, these restrictions apply only during the first thirty days, but not afterward. Summary: It is forbidden to greet a mourner with the greeting of "Shalom," or give a mourner a gift, within twelve months of the passing of his or her parent. It is permissible, however, to extend other greetings, and to greet a mourner with the greeting of "Shabbat Shalom" on Shabbat, and with the "Shalom Alechem" greeting customarily extended after Birkat Ha'lebana. In the case of the passing of another family member (as opposed to a parent), these Halachot apply only during the first thirty days.