As a department head, what to do if a professor leaves without giving out grades? I am department head. An adjunct professor teaching two courses in my department left without notice. He did not deliver the grades to me.

We have no staff in that field to give the final exam again. Even so, I wouldn't know how to convince the students to take the exam again, and I do not know what to do with the class activity, which should be part of the final grade.

The registrar is forcing me to deliver the grades, but I have no idea what to do.

Does anyone have any experience to share? What do department heads normally do in this situation?
I assume you've already tried to convince/pressure the instructor to provide enough information to assign grades.  Assuming he's not dreadfully ill, it would be incredibly unprofessional for him to refuse, but sometimes people are unprofessional.  If you don't know him well, is there someone else in the department who could try to talk some sense into him?  Was anyone else involved in the course, such as a TA or grader?

Once you've convinced yourself that you just can't get the grades, you need to take this up with the administration.  It's a really awkward situation, and you shouldn't be improvising a solution.  Whatever you do should be discussed with and approved in advance by the dean (or whoever has a similar level of responsibility in your university).  Presumably this issue has arisen before, and the previous decisions will serve as a precedent.  If this is the very first time, then you'll be setting a precedent.  Either way, you don't need to take sole responsibility for figuring out what to do, and you shouldn't.