How did the emperor approve the memorial?

Every dynasty is different. Everyone in the Tang Dynasty knew about it, so I won't say much. I would say Ming dynasty.

After officials attend the memorial, they are approved by the cabinet and attached with handling opinions, which is called a draft; After the draft of the ticket is submitted to the palace, it is generally handled by the eunuch of Li Si prison, which is called red; Finally, it was submitted to the emperor for examination and seal.