Shaykh Al-Albani was asked the following question:
When separating, oh Shaikh?
How about shaking hands when parting [i.e. from a brother]?
When parting, it is recommended to shake hands. However, it is not like when meeting. The Ahaadith reported on shaking hands when meeting are many and well-known. As for when parting, then there are a few, very precious Ahaadith. There is a Hadith in ‘Amal al-Yawm wal-Laylah of Ibn Sunni with a weak chain that the Prophet sallahu alayhi wa salam or his Companions – it is a long time ago [since I read it]- that when they separated, they used to send blessings upon the Prophet sallahu alayhi wa salam and shake hands. This is from the small Ahaadith which have been reported on shaking hands when parting. Due to their small amount, we differentiate between shaking hands when meeting, which is a Sunnah, and between shaking hands when parting, and it is recommended and a Sunnah”.
[Silsilatul-Huda wal-Nur no. 181]
Faisal Ibn Abdul Qaadir Ibn Hassan