There is a lot to say here on how to handle the situation I am sorry if this comes off as harsh.
NEVER Share your password with anyone. This was a bad decision from the start take this as a lesson to never give away a password to a private account to a stranger on the internet.
If you think any of us here have the power to do anything about the situation you are sadly mistaken as 1 we are not members of riot and 2 you have not posted any evidence or information. If your email asking riot for assistance was formatted exactly like this post I can see why they sent no response even though I do believe they should have just asked you to provide more information on this matter. If you really didn't give any of the information/proof through the email I highly recommend sending another to riot with the appropriate information that will at least get you moving in the right direction.
Also you should be clear on this but what exactly are the damages that this person caused? Did this person use your rp to gift himself skins? did he go into a game and troll? I am assuming you got the account back since this account features a 2015 mid season invitational summoner icon so I just want to know what damage he caused. If all he did was log into the account then log out or something like that just change your password block him and move on it really would not be worth trying to get this guy punished over that. If he took rp or trolled in a game which made you lose LP or receive a chat restriction then you are also out of luck because the account is your responsibility so you are responsible for giving away the information and letting this guy on your account. If he still has your account then assuming you have no way to recover it you need to be on top of this. Provide to riot your account information and describe the situation as best you can. The more information you give riot the more they can help you. I do not think this player will be receiving any punishments though as realistically this was all caused because you gave away your account information (I do not believe the IP hacks got him your password but saying he tricked you into thinking he is a friend is a strong indication you gave it up) however they definitely can help retrieve a hijacked account if you have the right information.
I almost forgot. If you had credit card information linked to the account and he used that to buy a lot of RP for himself then this is a whole new ballpark. I would make sure to include that in the report to riot (on top of actually canceling the credit card). Definitely let the bank or credit card company know that the purchases were not authorized by you and that an account online which has the information has been hijacked. I want to say the police should be involved too but I am not sure what they can do based on the fact you probably have no idea who this guy is.
Good luck with all of this