This one looks compleately different from the copies I've seen (and I have seen many of them), has this old style star (it looks better than on this foto - I think it's original), and has size of about 54-55. These feathures are unussual for a fake, but It looks too new to me.
I am not an expert in it, however the fabric and the style of sawing looks too new and modern. I think (it’s only my subjective opinion) it’s 100% fake.
I agree with Eric. This looks like one of those "made from old pattern but with new cloth" type of cap. The liner is probably in unused condition.
One of the ways to check authenticity is smelling. But the problem with Russian uniforms is that they often have covered them in moth balls. That and the very common eue de colonge smell, or that's perhaps a way to hide the new smell lots of fakes have....
It does look way to new and with odd stitching in this image. Any signs of aging? Why no fading? What does the lining look like? You can test the thread under black light - synthetic will glow and should not be on a budenny of this era. However, modern cotton won't glow.
I didn't have much hope for this.
Only the star looks "old" (minor damage and it's a little dirty what's not visible on the picture).
I'll consider it fake and simply sell it as one.
THanks.