That was my concern too. I wasn’t even sure that it was even possible for a professor to change a grade this long after the semester is over. It’s also problematic because it’s hard to really think of a reason/excuse why this is being discussed now, after the course is over, if it wasn’t mentioned at all before grades were in. The letter makes it sound as if the student was struggling the entire time; it wasn’t as if the final exam was the first bad grade.
I think it honestly makes more sense to work on an appeal just because it might be hard to get an incomplete at this stage even if the professor was willing to assign one and it might be hard to justify one this long after the class ended.