Well, first of all, the SI has to figure out how to access Penny's memories properly. It could be that the memories are stored in a way that's not immediately intuitive for the SI. Once they start accessing them, they might find that some memories are painful, like Penny's experiences of being ostracized because of her synthetic nature. The SI could choose to confront these memories head - on, using them to better understand Penny and grow as a character in the fanfiction. Or they might try to suppress some of the more difficult memories, which could lead to its own set of problems later on.
The SI might initially be confused by Penny's memories. They could be like a jumbled mess of information about Penny's past experiences, friendships, and her role in the RWBY world. Some SIs may choose to embrace these memories fully, using them as a guide to navigate Penny's life. Others might struggle with them, trying to separate their own identity from Penny's while still having to deal with the memories that come with her form.
In a RWBY SI Reincarnated as Penny fanfiction, the SI's handling of Penny's memories is a complex matter. Penny had a lot of memories related to her interactions with Ruby and other characters. The SI may use these memories to form stronger bonds with the characters Penny already knew. However, they also have to be careful not to let Penny's memories overtake their own sense of self. They might start by cataloging the memories, trying to understand which ones are important for maintaining Penny's relationships and which ones are more personal to Penny's development. Some SIs may even try to rewrite or modify Penny's memories, but this could have unforeseen consequences within the story's universe.