How to convince someone to see a neurologist?

If this happened last year, and changed followed on quickly, the damage may be done.
There may have been a hematoma pressing on a vital center.
In recent falls this is handled emergently with drilling of a burr hole to release the bleed.

I would move her by telling her that there may have been a small brain bleed under there pressuring the brain and she should have a scan to ascertain this. Explain the sudden changes you saw after this fall and tell her there is a chance a scan can show an area pressured in her brain.

In all truth, what damage was done from a year ago in time is too late to address now. Any bleed will have done what damage it did do. But a scan would be useful in differentiating reason for her changes.

I think you need to approach it as a follow up to her concussion. Tell her this is a little long to still be having the problems she is. That a Neurologist will look into why.

ALZ is not caused by a concussion. Even though its under the Dementia umbrella, it effects the brain differently. Usually inherited.

My personal opinion is that an accurate diagnosis helps determine what treatment a person receives, and what expectations to have for them and any recovery -- or not. This applies to dementia. The diagnosis is not only for the patient but also for the family or whomever is going to be managing her affairs and making decisions on her behalf.

Due to your friend's advanced age, it may not be possible to determine what's actually going on with her, but a scan may reveal she had a brain bleed from the fall, or maybe she had an unrelated stroke at some point, or she has a form of dementia.

It's possible that your friend may be willing to go to a doctor if you go with her, since you may be less intimidating than her family. But you should work with your friend's family (discretely) to see if they want you to help in this regard, and to also communicate any outcomes of an appointment. You would definitely need to go into the exam room with her, and be present when anything discussion is had between her and her doctor. Make sure your friends knows that "if it was me, I'd want to know for the following reasons..."

There's a strategy called a "therapeutic fib", where we tell our LO a harmless lie in order to incentivize them to do something that's in their best interest. Hence the suggestion by Grandma1954 to use the Medicare Annual Exam as a motivator (implying that the exam is both "required" and free).

I wish you all the best as you help her navigate this situation!

There can be long lasting effects from a concussion. Some lasting a year or more.
If she has not had a follow up after the concussion that should be done.
I would approach it as a "concussion" follow up. Nothing more.
Since we are now starting to get all the information about insurance and "open enrollment" is soon I would also suggest that she have the "Medicare Annual exam"
Now that I have said all that...
This is a friend.
You are not a relative.
I am assuming you are not POA or Guardian
Say your piece then let it go.
To see a doctor or not is her decision

Let her know that you support her
Let her know that you will be there for her if she needs it.
Let her know that you are going to let the matter drop, that you are not going to hound her any more.
You can't do more than that.

(but if you are out together and she gets dizzy or shows signs of confusion you are within your right to tell her that you feel that she should go to the emergency room)

It may NOT be Alzheimer's or any form of dementia. I just did a quick medical literature search; forgetfulness is a common long-term effect of concussion in people of every age. Won't know for sure until it's checked out.

So encourage her to get a follow-up visit about the concussion. People go to cardiologists for their heart, ophthalmologists for their eyes, and pulmonologists when their lungs aren't working right; so why not see a brain specialist about a hurt brain?