If the soul is reborn, how does śrāddha reach my ancestors?
tradition says the offering reaches them in whatever form they are, carried by the pitṛ-devatās; and it purifies the giver too.
This is an old and fair question, and the texts answer it. The Purāṇas describe divine beings, the pitṛ-devatās (such as Aryamā and the Vasus, Rudras and Ādityas who preside over the three generations), who receive the offering and convert it into what nourishes the ancestor in their present state. If they are born as a human, it becomes food or comfort; if in another realm, the corresponding nourishment. An old image is a calf that finds its own mother among a thousand cows.
Vedānta traditions add that śrāddha is also for the living: it expresses gratitude, unites the family, feeds the needy and purifies the mind of the giver.
Different schools hold different views, and no one can prove the mechanism. But every tradition agrees that remembering ancestors with love is good karma. You can do śrāddha in that spirit without needing every metaphysical question settled.
Source: Matsya Purāṇa; Garuḍa Purāṇa
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