This is something which has been asked for a number of times & when I looked at it again today, it didn't look possible.. indeed, the author is a read-only element of the content update service. However, hidden away in the code and not documented (AFAIK) is a way to update the author via a JSON PATCH operation!
Here's how you can set it up;
Set the content type to application/json-patch+json;charset=UTF-8, e.g.
The format of the payload is in the JSON PATCH format, which is explained nicely here; JSON Patch | jsonpatch.com
So now you can write admin pages or scripts that call this API to change the author across multiple documents.. yay!!
The only downer is that this only works with Documents <shakes fist>