"Well, I guess I can let you do it."
Prince Lucien returns the documents back to Penelope and sits on the vacant chair in front of her desk. It means he is only allowing her to sign the documents. And after that, Penelope will give the documents to Prince Lucien so he can start keeping them inside the vault. With a sigh, Penelope writes her name and signature on the documents.
While doing it, Penelope noticed that she is already used to signing her name on the documents. When she first handled the documents left on her father's desk, Penelope is only using an official seal to approve those acceptable plans written on it. But there are some documents that need a written signature on them. When she asked King Galia about it, the king told her to sign it with her name instead since she is temporarily holding her father's position.