Is it permissible to make up missed prayers for the deceased during their final illness, and what is obligatory towards the deceased if making them up is not permissible?

One who dies with unperformed obligatory prayers should not have them compensated on their behalf. The fundamental principle regarding acts of worship is that vicarious performance is not permissible unless there is a specific textual injunction allowing it, and no such text exists for prayer. Ibn Umar (may Allah be pleased with them both) said: "No one prays on behalf of another." The son's duty towards his deceased father is to supplicate for him, seek forgiveness for him, execute his will, honor his friends, and maintain kinship ties. The best things a child can offer to their deceased parent are supplication for them and ongoing charity (Sadaqa Jariya).