Wa alaykum salam wa rahmatuLlahi wa barakatuHu,

In both Bukhari v. 1, p. 318 and Muslim v. 7, p. 21, the Prophet Muhammad performed the funeral prayer for the Ethiopian king, Najashi (rahmatullah ‘alayh). Based on this, the Shafi’is ruled that the funeral prayer may be performed for one absent from the country [balad], as the Prophet Muhammad was in Hejaz and Najashi in Ethiopia when it took place. (Sharh al-Muhadhdhab v. 5, p. 251-53)

Not only is this ruling the relied-upon position of the Shafi’i School, more decisively, it is the practice of Allah’s Messenger (sallallahu ‘alayhi wa sallam) as established in the ahadith sahihah (authentic narrations), like what Imams Bukhari and Muslim related.

In conclusion, the practice mentioned in the question is valid and is the Sunnah of the Prophet Muhammad (sallallahu ‘alayhi wa sallam).

And Allah knows best.