"I received this diamond from my grandmother."
Tell me if I'm wrong but I believe 祖母にこのダイヤモンドはもらいました is bringing more attention to "this diamond" as if someone asked "what did your grandma give you?" while このダイヤモンドは祖母にもらいました seems more like the answer to "who gave you this diamond?" emphasizing "my grandmother". In my language, Italian, there is a similar system, although with some other complication to it