The second takbir is followed by sending blessings upon the Prophet ﷺ; the familiar Abrahamic blessing is used in Hanafi practice.
The supplication after the third takbir is a separate step, focused especially on the deceased and on Muslims.
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The place of blessings on the Prophet
Funeral Prayer: Leadership, Four Takbirs, Supplications and Salam
The second takbir is followed by sending blessings upon the Prophet ﷺ; the familiar Abrahamic blessing is used in Hanafi practice.
The supplication after the third takbir is a separate step, focused especially on the deceased and on Muslims.