No you cannot transfers Google Authorship from one account to another, there is no such mechanism to tell Google about such a switch.
You could of course simply change the rel=author tag like you have mentioned, but this is not recomnded unless for some reason the former employee becomes a public disgrace, or simply starts moving in directions that will not enhance there reputation in your industry.
There are many reasons to keep the same author even after leaving the company. If the former employee continues to build a great reputation in your industry after they leave, then that reputation continues to work for your content.
Keeping Google Authorship / rel=”author” ensures that author rich snippets persist, which can increase click-through rates.
No AuthorRank is lost, thereby potentially increasing its search rankings.
If you remove it, the former employee may become disgruntled that their content is now being attributed to another. This could cause a PR/social media headache for the former employer.
Also it's unethical to simply attribute content that was written by one person, to some one else.
These points and more are covered below: (there are 3 separate links, but i cant seem to get them to go on a separate line)
Why Your Brand Shouldn't Fear Assigning Authorship
4 Reasons Why You Shouldn't Remove An Ex-Employee’s Rel=”author” Tag
Google Authorship and Former Employees