M34 German Fire Police helmet

I found this yesterday advertised as a WWII issue helmet. The price is reasonable if real at $120.00 but I can't make a determination on authenticity.

It's a real fire police helmet, it's an M34 but beyond that, no luck. From what I can gather, not all of these were marked. Those not marked are generally accepted as being postwar. This one is marked but not in the traditional manufacturer/size combat helmets are marked. It only appears to have a manufacturers logo that is a T inside a diamond at the rear of the helmet.

I'm leaning towards this being a post war helmet for several reasons, the smooth transition around the lip rather than the more squared appearance with most wartime helmets and the color and quality of the liner. It is dark, stiff and thin rather than tan and more flexible. But would appreciate those with more knowledge helping me out on this. If it's genuine WWII, I'd like to add it to my collection. It has cork spacers and is missing the chin strap. This type helmet was issued with no decals during the war so it remains possible. Transition to this type rim occurred late in the war from what I understand.

Condition is excellent and paint appears to be original from first hand inspection. I have a limited time frame to get this at this price and then it goes back up to $150.00

https://www.milsurps.com/images/impo.../mTae3zO-1.jpg

https://www.milsurps.com/images/impo.../r80lMXz-1.jpg

https://www.milsurps.com/images/impo.../QwxTjzJ-1.jpg

https://www.milsurps.com/images/impo.../rNOn7TH-1.jpg

https://www.milsurps.com/images/impo.../3vZnUg5-1.jpg