Oldies jazz song in Harry Potter and the Prisoner of Azkaban

When Lupin is saying good bye to Harry at the end of the movie in his office, there is a song playing in the background:

[8m-UsVyqzZg]https://www.youtube.com/watch?v=8m-UsVyqzZg[/video]

it might be part of John Williams - Swing,swing,swing https://www.youtube.com/watch?v=MGpY3pe3kMk or longer version here https://www.youtube.com/watch?v=e4UGvont-j8