$13,000 for one carat? If it's man made, it's cubic zirconium, worth about $10 when mass produced.
What makes diamonds worth their inflated price is the time it took nature to produce them plus the 4 Cs:
Color, Clarity, Carats and Cut.
In Grandma's last days, she didn't have good color, and her mental clarity was nill. She didn't like carrots, and was never much of a cut up at parties.
You should be able to deduct about 12 grand right there.