Does the Lich share a consciousness through all parallel forms?

I've seen this discussed and for a long while it seemed to be true, the OG lich, farmworld and the hands all shared memories or a consciousness but I haven't found any true confirmation, and F&C season 1 kind of flipped this on its head with Extinct World lich. The only possible explanation I can think of is that EW lich is an outlier and is "cut off" from that consciousness, maybe due to prismo. I don't know, would love to know if there's any mention of it in canon material.