this sounds veeery fishy to me.
You can t get an account unbanned if there are no appeals left.
You can t just email Jagex like "Hey I love you, blah blah blah."
unless your offering an appealing service which i dont really think is allowed, then this is a scam because once an appeal is denied you cant do anything, however i will say if you are a runescape moderator then you can go to mod center and go to the forums there and ask for an appeal although mods get told of for posting for others....