Grading: This hadith is "sahih li-ghayrihi", while this chain is weak because of al-Khalil bin Murrah, and he was contradicted in narrating it as connected.

Reference / Source: Ibn 'Adi (3/ 59), Tammam in "al-Fawa'id" (724) and al-Bayhaqi (6/ 218) narrated it via various routes from 'Abdullah bin Wahb with this same chain. They added in it: "And the people of two (different) religions do not inherit from one another."

Technical note / Defect ('illah): Al-Khalil was contradicted by Ibn Jurayj [in 'Abd al-Razzaq (9870, 19002, 19314, 19315)]; he narrated it from 'Amr bin Shu'ayb, from the Prophet (peace and blessings be upon him) as "mursal". In some of them he added: "(It goes to) whatever relatives he has of the people of his religion; and if he has no heir, the Muslim inherits from him by virtue of Islam."

Reference / Source: Abu Nu'aym narrated it in "al-Hilyah" (7/ 318) via Sa'id bin 'Amr al-Ash'athi, from Sufyan bin 'Uyaynah, from Ya'qub bin 'Ata' bin Abi Rabah, from 'Amr bin Shu'ayb, likewise. And he said: "It is gharib as the hadith of Sufyan from Ya'qub, and no one narrated it as connected except Sa'id."
Technical note / Defect ('illah): We say: Sa'id al-Ash'athi is thiqah, but his narration contradicts the wording of the narration of "the group" from 'Amr bin Shu'ayb [among whom is Sufyan bin 'Uyaynah: Sa'id bin Mansur (137), Ahmad (11/ 6664), al-Nasa'i (6351) and others]; so the blame for it falls on Ya'qub bin 'Ata', because he is weak.

Reference / Source: The narration of the group from 'Amr bin Shu'ayb, from his father, from his grandfather, as marfu', has the wording: "The people of two religions do not inherit from one another." It was narrated by Ahmad (6664, 6844), Abu Dawud (2911), Ibn Majah (2731) and al-Nasa'i (6350, 6351) via various routes from 'Amr bin Shu'ayb.

Corroborating chains and supporting reports: On this topic there is a narration from Usamah bin Zayd (may Allah be pleased with them) in al-Bukhari (6764) and Muslim (1614).