Is the Hadith, "When two believers meet and shake hands, Allah interposes His hand between their hands, Allah Almighty turns His Face towards them, and their sins fall away from them as leaves fall from a tree," authentic, and who narrated it?

The hadith with the exact wording mentioned was not reported, but authentic hadiths with its meaning were reported, among them: "There are no two Muslims who meet and shake hands, but they are forgiven before they separate," and "Indeed, when a Muslim shakes hands with his brother, their sins fall away, just as the leaves of a tree fall." Also, a weak hadith was reported on the authority of Anas (may Allah be pleased with him) with the wording: "There are no two servants who love each other for the sake of Allah, one meets the other and shakes his hand, and they invoke blessings upon the Prophet (peace and blessings of Allah be upon him), but they do not part until their sins, past and future, are forgiven."