You can read more about the turbulent history of this famous
diamond, below, where Nadir Shah's assassination is mentioned.
You can also read more about Nader Shah, below, where you can
find mention of the diamond, but with no mention of how he handled
it once it was in his possession.
One could assume that he simply enjoyed it, given these two
sources, beginning in May 1739, when Nader Shah left India with the
diamond, and his assassination in 1747.
Its further history is available in the link named
Koh-i-noor.