Yesterday I bought some brackets to try to fix it with the solenoid.
Today I managed to complete the task.
I tried 2 different spot on the helmet to secure my solenoid to, at the top and at the back.
The top one is fine but it is difficult to mount the bracket as there is not even surface as shown. Hence it was hard to get it straight and thus I failed to make it straight.
However, placing it at the back was so much easier and it actually is better because I plan to hang the helmet anyway. I also decided to drill a hole in order to let the wire run inside of the helmet.
I fastened the solenoid to the bracket with 2 small black cable ties. It worked really well actually.