Question: Is it effective for Buddhists to dedicate Merits to the deceased if they are not Buddhists?
Answer: Merits can be shared with anyone (deceased and alive) – for betterment of their lives, for aiding a better rebirth, for connecting them to the Triple Gem… However, the form and extent of the benefits the deceased can receive differs according to their conditions.
For example, if we wish to share Merits with someone to help him or her be reborn in Pure Land, the three provisions are needed by that person – Faith (in Amitabha Buddha), Aspiration (to be born in Pure Land) and Practice (Mindfulness of Buddha).
According to the Amitabha Sutra, birth in Pure Land requires Good Roots (Shan Gen), Good Karma/Merits (Fu De), and Karmic Affinity (因缘 or Casual Conditions) too. When this trio is in lack, even when there are much Merits (a requisite above) dedicated to the deceased, the person is unlikely to give rise to the three provisions.
However, it is possible that the deceased hear and understand the Pure Land teachings and thus give rise to the three provisions. To help effect this (by spurring growth of their Good Roots, creating Merits in their name by doing good and creating Karmic Affinity for the Pure Land teachings), we can chant Amituofo’s name and/or Amitabha Sutra more and dedicate the merits directly for this cause. Hopefully, this will inspire rise of the three provisions.