However, the fact that Rika is aware that a version of herself exists in a higher dimension, that she says she isn't Rika when she's speaking to Rena in Tsumihoboroshi-hen (Bernkastel feels that way to an extent) and that she gives herself the name Bernkastel when inhabiting Rika's body in Saikoroshi-hen to distinguish herself from the original Rika indicates that the Rikas of the various worlds possess at least some of Bernkastel's memories. Conversely, in Minagoroshi-hen Bernkastel says that she only has the memories that Rika obtained from the various worlds, that she was born in the human world and refers to herself as Rika at one point. Based on that, as well as all the things she says in the tea parties in Umineko which make it clear she was born from the events in Higurashi, we can assume that Bernkastel views herself as an being that's a continuation of Rika rather than a completely separate entity, which supports a close connection between them.
When Rika dies, Hanyuu sends the memories from that world to join the accumulation of memories in that higher dimension and thus become part of Bernkastel. This would explain why Bernkastel retains the name that "Rika" came up with in Saikoroshi-hen and why the Rika in the world at the end of Saikoroshi-hen says that the version of her in the higher dimension no longer matters, since her memories won't be joining it when she dies.
So in conclusion, a copy of Bernkastel's memories and personality replace Rika's mind and then the experiences of that copy merge with Bernkastel when the Rika of that world dies. Bernkastel neither created Rika nor is she really a separate entity (since 'Rika' is simply Bernkastel's mind in a human body) until they diverge at the end of Saikoroshi-hen.
