The Rebbe's guidance on grief, on the eternity of the soul, and on how to honor someone who has passed away:
The soul lives on. The soul is eternal; the departed soul remains present with those close to it and continues to ascend (IK 567, 7433). Belief in the eternity of the soul means one must not mourn excessively — the Torah sets limits to mourning, and one must balance mourning with continuing life (IK 6307, 9804). On the stages of death and resurrection, see IK 170; on the resurrection itself, see Moshiach and Geulah – The era of redemption.
Turning grief into action. The true way to honor a loved one is to channel grief into positive deeds, which benefit both the mourner and the departed soul (IK 7620, 9955). Honoring a departed parent is best done by actively living and spreading the values he or she stood for (IK 5896). Strengthen Torah and mitzvos after a loss (IK 9506, 10863, 8630, 2216); learning Chassidus and giving tzedakah bring elevation to the soul (IK 9337, 10193). True love is rooted in essence, not merit, and grief and memory should lead to action (IK 8466).
Comfort. True comfort after loss comes through Torah wisdom and faith (IK 1463, 1128). Consolation after loss unfolds in stages, and G-d's comfort is not only doubled but elevated (IK 178, 5859). The traditional words of comfort link personal loss to the mourning for Zion and Jerusalem — and so to the assured comfort of the redemption (IK 8835, 9211, 9216). Sharing grief with others brings comfort and unity (IK 582). Don't blame others for a misfortune; trust in G-d's ways (IK 1638), and see Bitachon – Hardship, loss and asking why.
Consoling others. Comforting mourners by letter fulfills the mitzvah of nichum aveilim (IK 9266). Offer comfort together with practical help where needed (IK 8995). On responding to communal tragedy, see IK 7217, 9933.
See also: Bitachon – Hardship, loss and asking why; Mourning and loss – Kaddish, yahrzeit and the tombstone.