Selling kei car but didn’t changed plates

Hi everyone,

I'm moving out of Japan in December and have decided to give my kei car to my cousin that lives in Shizuoka, I lived in Toyokawa and my plates were from Toyohashi,

earlier this year, I've moved to Fukui but never changed my plates, and now my cousin is asking me if I'm going to declare leaving Japan in the city hall, as she thinks that I have to be registered at a valid address at the time of the ownership transfer,

so, my questions are:

1. Do i need to transfer my plates to Fukui before giving the car away?

2. Do I need to transfer the car ownership before I declare leaving Japan in the city hall?

Thanks in advance!