Has anything been reported in the Prophetic Sunnah to the effect that when a Muslim greets another Muslim or shakes his hand, Allah Almighty forgives them both before they part?

Greeting others and shaking hands are among the praiseworthy sunnahs through which Allah Almighty forgives sins. This is established by the Prophetic Sunnah:

• Al-Bara’ ibn ʿAzib (may Allah be pleased with him) narrated that the Messenger of Allah (peace and blessings be upon him) said, “Whenever two Muslims meet and shake hands, their sins are forgiven before they part” (recorded by Ahmad in Al-Musnad, Abu Dawud, at-Tirmidhi, and Ibn Majah in their Sunan, and by Ibn Abu Shaybah in Al-Musannaf).
• Hudhayfah ibn al-Yaman (may Allah be pleased with them both) narrated that the Prophet (peace and blessings be upon him) said, “When a believer meets another believer, greets him, and shakes his hand, their sins fall like the leaves falling from a tree”
  (reported by at-Tabarani in Al-Muʿjam al-Awsat and Ibn Shahin in Al-Targhib).
• Anas ibn Malik (may Allah be pleased with him) narrated that the Prophet (peace and blessings be upon him) said, “Whenever two servants of Allah who love one another for the sake of Allah meet, and one greets the other, shakes his hand, and both send greetings and blessings upon the Prophet (peace and blessings be upon him), they do not part until all their past and future sins are forgiven”
  (recorded by Abu Yaʿla al-Mawsili in Al-Musnad, Ibn al-Sunni in ʿAmal al-Yawm wal Laylah, al-Bayhaqi in Shuʿab al-Iman, and al-Shajari in Tartib al-Amali).

And Allah Almighty knows best.