Help with Kitchen Hood controls

[gutierrjgELE22]

Hi to all!
I would like to add a remote fan to a kitchen exhaust fan. I need to be able to turn it on/off from any of the first three speeds that the kitchen exhaust has. I already have relay to control that remote fan but nut sure how make it work. as you can see in the image attached the controls has Blue for High, Brown for Med, Gray for low speed.
Any help will be appreciated.
Thanks