I have one single cartridge of this.
Just a bit longer than the std 6,5x55
It has the measures like the 6,5x58R Sauer, but
the shape of the 6,5 x 53,5 Daudeteau.
Actual case lenght is 56,5 mm
Rim Ø is 13,23 mm
HS could be Czech ?

Roy, it is Czech.
Click on Reference above. Then on Headstamp Codes. Scroll to PS. Four choices, and I’d say yours is the last one. (I’m familiar with the last 3.)

PS Giulio Fiocchi S.p.A., Lecco, Italy 1
PS Pirotecnia Militar de Sevilla, Sevilla, Spain 1
PS Poongsan Metal Manufacturing Company Ltd., Seoul, Republic of Korea (probably at the Angang Ammunition Plant) 2
PS Povázské Strojárne, Povázská Bystrica, Czechoslovakia (now Slovakia) 1

Thanks Dan,
from my Cartridge Guide by Ian Hogg, I thought this HS could be the ‘Slovakian’ one, still I am most
uncertain about the caliber…

I believe it is what it says. 6.5x57R

6.5 x 57 R was a quite popular hunting caliber in central Europe, a rimmed version of the 6.5 x 57 introduced around 1893. It was never a military catridge.
PS made this cartridge with 6 different bullets. Yours (tip is not visible) could be the 10 g or 10.5 g FMJ round nose bullets or the 10 g soft point version.
The PS factory is located in Slovakia, but was of course a Czechoslovak company at the time.

Thanks JPeelen,
interesting news to me!
The actual bullet is a flat hollowpoint, with the steel going all the way
to the hollow point

Lancaster there are a good number of mistakes in that Ian Hogg book, so double check. Which you apparently are doing & just letting you know.

Thank you !
Although the book is ‘OK’, yes there are errors, so when in doubt i double check.
This forum is very good for references!