Prophet (SAW)'s Prayers

When the soul has left the body
اللَّهُمَّ اغْفِرْ لِفُلَانِ وَارْفَعْ دَرَجَتَهُ فِي الْمَهْدِيِّينَ وَاخْلُفْهُ فِي عَقِبِهِ فِي الْغَابِرِينَ وَاغْفِرْ لَنَا وَلَهُ يَا رَبَّ الْعَالَمِينَ وَأَفْسِحْ لَهُ فِي قَبْرِهِ وَنَوِّرْ لَهُ فِيهِ
"O Allah, forgive (name of the dead person). Make him among the guided ones, raise his status and be his deputy among the grieving. O Lord of the two worlds, forgive us and him and make his grave wide and full of light". Prophet Mohammad (SAW.) recited this dua after the death of Abu Salama (R.A.) after closing his eyes. In place of فُلَانُ state the dead person's name.

(Mishkat from Muslim)
When recited for another Muslim then in place of فُلَانُ mention the name of the dead person and before the name add a "Laam" with a "Kasrah (Zer)"