Abdullah bin Amr traced this saying back to the Prophet ﷺ, who said, "The merciful are shown mercy by the Most Merciful. Show mercy to those on earth, and the One above the heavens will show mercy to you."
يبلغ به النبي ﷺ قال: الراحمون يرحمهم الرحمن از حموا أهل الأرض يرحمكم من في السماء.
Abu Dawud (4941) and Tirmidhi (1924) both narrated it from the hadith of Sufyan, from Amr bin Dinar, from Abu Qabus, the freedman of Abdullah bin Amr, from Abdullah bin Amr, and he related it, with the wording given here being Abu Dawud's.From this same route, it was also reported by Imam Ahmad (6494) and Darimi in Radd Ali Jahmiya (69), and Hakim graded it sahih (4/159). Some narrators added, after his words "the One who is in heaven," the phrase, "Kinship is a branch of Rahman, so whoever maintains it, Allah maintains ties with him, and whoever severs it, Allah severs ties with him."Tirmidhi said, "hasan sahih," and Hakim considered this hadith and everything else on this subject to be sahih.I say, it is only hasan, because of Abu Qabus. Ibn Hibban mentioned him in Thiqat (5/588), Ibn Abu Hatim gave his biography in Jarh wa Tadil (9/589), and so did Bukhari in Tarikh al-Kabir (7/194), but he does not rise to the level of being considered trustworthy. Still, there is no harm in relying on him as a corroborating witness, since what he transmitted agrees with what the trustworthy narrators report. That is why Tirmidhi and Hakim both graded it sahih. Dhahabi said in Mizan, "He is not known," yet he affirmed, in Uluw (14), Tirmidhi's grading of it as sahih.