This item did not often encountered, a standard issue Wehrmacht headlamp (Strinlampe) designed to be fits on German M35, M40 and M42 helmets.
This is a fun restoration (will be post separately) and happened to have straps and 5mm cable around, the strap is not well design if it did not wrongly made, quiet easy to slip off.
There is a standard 12V bulb for period touch (flashlight) the housing has a clear plastic and a blue filter to soften the light.
The 24mm strap link with an elastic band and a D ring or O ring, joint to the other side by a hook.
It is link by a two core cable round the helmet to a battery box with power switch, a 12V rechargeable battery is just fits in it.