´It was narrated that Anas bin Malik said:` "The Messenger of Allah milked a sheep and drank some of its milk, then he called for water and rinsed his mouth and said: 'It has some greasiness in it.'"
Related hadith on this topic
Explanation & Benefits
Shaykh Umar Farooq Saeedi
Benefits and Issues:
It is recommended (mustahabb) and superior to rinse the mouth after drinking milk; however, if one does not do so, it is still permissible.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 197