[af_vet_1981]

An Apochryphal book does allude to praying for the spiritual benefit of dead brethren. This is a long standing Jewish tradition (Mourners' Kaddish, which is a magnificent prayer). The Catholic tradition likely came from the Messianic Jews but there is no Apostolic scriptural support or teaching other than perhaps 1 Cor 3. I cannot recall Jesus commenting on it directly (unless Let the dead bury their own dead with respect to reburial applies, but this is well after the standard seven day Shiva).

[Former Fetus]

I agree, the Kaddish is a beautiful prayer, but if you read the words carefully it does not mention any spiritual benefit for the dead person.

May His great Name grow exalted and sanctified
in the world that He created as He willed.
May He give reign to His kingship in your lifetimes and in your days,
and in the lifetimes of the entire Family of Israel,
swiftly and soon. Now say:
Amen. May His great Name be blessed forever and ever.
Blessed, praised, glorified, exalted, extolled,
mighty, upraised, and lauded be the Name of the Holy One
Blessed is He.
beyond any blessing and song,
praise and consolation that are uttered in the world. Now say:
Amen
May there be abundant peace from Heaven
and life upon us and upon all Israel. Now say:
Amen
He Who makes peace in His heights, may He make peace,
upon us and upon all Israel. Now say:
Amen

As for the Apochryphal book (2 Maccabbees?) to me it does not carry the weight of Scripture.