Cartridge Identification

I Know absolutely nothing about Bullets or firearms But have had good luck with collectors forums in the past I am sure some helpful soul will be able to help me out here.
My uncle died many years ago and in his belongings he had a “swagger stick” that he came back from Europe with (WW1) not sure if it is British, German, or other I am hoping that if the bullet can be identified I can tell from that…
Any help is appreciated I hope the picture uploads correctly

the pointed end of the stick is the tip of a bullet, the other end of the stick is the bottom of a bullet
There are marks on the end (i think you call that a headstamp)

Unfortunately, I think the cartridge may not point to the nationality of the owner of the Swagger Stick, because it culd have been made by, or as a gift for, whomever carried it.
The cartridge coud have been issued to a soldier, or a battlefield pick-up.
Just guessing from photographs I have seen, British officers were more likely to carry one, from the Zulu battles through WWII, Korea, and Vietnam.

Would the headstamp be Danish?

Can you get a close up of the headstamp?

Headstamp as close as i could get
hs1

F A 4 10
Frankford Arsenal, made in 1910.

And the caliber is .30-06, as used in the Springfield Model 1903 and Model 1917 (made by Winchester and Remington) rifles issued to American troops during WWI.

Thank you all for your support,
at least I know it was made with a very common shell

Yep, Alex and Fed beat me to the punch. I suspected an “F” and not an “H”. The 4 10 means April 1910.