Ancient treasures created by those predecessor cultures are not owned by the people who destroyed the culture they come from. They literally have no connection. Not culturally, and to a large degree not even genetically.
It would be like saying that ancient Native American art is rightfully owned by the Kennedy family.
So that's the moral side.
On the practical side - what a terrible idea, to send irreplaceable ancient human cultural artifacts to be kept in such an unstable, low-trust society. They will not be good stewards. If we care at all about people in future centuries and millennia being able to see these objects, they need to be kept in the most stable countries.