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.