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Well...
I'm not entirely sure what you're asking. You're asking if it's a fake. A fake what?
If you think it's a violin made by the famous Antonio Stradavari it most definitely is not. It's not even claiming to be made by him. The inside of the violin says Antonius Stradiurarius Cremonensis. It also says that it was made in Czechloslovkia, and Antonio Stradavari was Italian.

Also, this violin was not made in the 1700s, but rather the mid to late 1800s. The label is most likely mimeographed (sort of like an old xerox). Actually, the violin could even be younger than that. It's hard to tell from the pictures. If I could look at it in person I would be able to tell a lot more about it. When I first looked at the violin I thought it was perhaps German because it is so wide and thick. That it is Czeck makes sense. During the 1700s violins were much thinner, especially at the neck. It appears to be very thick and wide everywhere, and the back bulges out. When I read that it was only a 3/4 size violin I was surprised because typically 3/4 size violins look more delicate than that. Another reason I feel it was made during the late 1800s is the wearing of the violin. I would guess that very few people have played this violin. Perhaps only one or two people other than your Grandmother. The people who have played it apparently did not play it very often, or if they did they wore gloves. The varnish is hardly even worn, not even in the places it is typically worn by moderate use. My violin was made in the mid 1800s and the varnish has worn considerably.

How long has it not had any strings on it? It looks as though it has not been played in decades. It is a very bad idea to store a violin without strings on it. Violins are made for the pressure, and without the tension from the strings the wood shifts, loosens, and warps. Sometimes the soundpost can fall over. Also, if you don't play a violin for a very long time the wood looses its ability to vibrate. The value of this violin has been damaged by the way it was stored, I can tell just by looking at it.

I'm sorry if any of this is disappointing.

It has veen a very common thing over the centuries to make copies of the famous Italian baroque violins. It always makes me laugh when I see an amateur Eastern European's attempt. The funniest one was a German attempt. The varnish was so dark it was almost black.

I am not entirely confident with my evaluation as I can't actually see the violin in person.
When we went in to get my violin looked at the guy taught me a lot about identifying violins.