It is narrated from Hisham bin Urwah (may Allah have mercy on him) that I have seen several letters of the Prophet (peace be upon him) in which, when a matter was concluded, "Amma Ba'd" was written there.
Hadith Referenceالادب المفرد / كتاب الرسائل / 1121
Benefits and Issues: The point is that just as the phrase "amma ba'd" can be used in a sermon (khutbah), in the same way, using the phrase "amma ba'd" in writing is also Sunnah.
Source: Fadlullah al-Ahad: Urdu Commentary on al-Adab al-Mufrad, Page: 1121