Why Catholics keep praying after the funeral.
Eternal rest grant unto them, O Lord, and let perpetual light shine upon them. May they rest in peace. Amen.
Have Masses offered for the dead. Ask at the parish office; this is the greatest thing that can be done for them.
November, and especially All Souls on the second of November, is the month set aside for it.
The communion of saints means the Church is not divided by death. Those being purified can be helped, and the help travels in both directions: we pray for them, and the saints pray for us.
Second Maccabees describes prayer and sacrifice offered for the dead so that they might be freed from their sin, and the earliest Christian inscriptions in the catacombs ask the living to pray for the buried.
The practice is universal and ancient, kept by Catholic and Orthodox Christians alike, and predates any later disputes about it.
Praying for the dead is a work of mercy and part of the faith, not an optional devotion. How and when you do it is yours.