Where can an academic put their lecture slides for posterity?
Archive.org (not to be confused with arxiv.org) aims to be the world's library. According to its FAQ,


  The Internet Archive focuses on preservation and providing access to digital cultural artifacts


It cites the destruction of the Library at Alexandria as the kind of loss of cultural heritage which it aims to avoid, so preserving an academic's teaching material should be perfectly aligned with their goals.

The FAQ also has a large section on uploading content. I suggest you pass that URL along to your colleague.