I was never sprited and I am sure it happened to people different ways in different timelines. My memory is that sprites with multiple people prototyped into them formed a gestalt entity similar in some ways to a gem fusion. The gestalt sprite had the past memories and intentions of both/all parts, but formed a new identity moving forward, which included the intentions of the skaia-sprite-construct.
My guess if you had a kintype who had become a sprite during their timeline is that you would have a fair amount of the rest of the other member’s memories. I think it would depend on what exactly the circumstances were. I know that some people have kintypes that are sprite gestalt entities (davepetasprite, for instance) and some people have kintypes that simply were a part of sprite gestalt entities and no longer are. (Nepeta who had been a part of davepetasprite).