I'm not a lawyer, but IMO if Grandpa had left it for Granddaughter then no transfer docs would be required. But it seems it is now owned by Grandma. So, Grandma would need to get it to an FFL.
If she's in northern NJ I can recommend:
http://www.gunshopfinder.com/bytownresults.asp?ID=4223
The above site allows you to search by town.
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