Hello Overmann,
Uh, I could not even find a single picture of the Videocomp VES-TWO genlock on Google, I only found some information about the
VES ONE.
As far as I understand,
PREH is a German manufacturer which now focuses on
automotive parts and electronic systemsNow let's find replacemement parts.
Check out this one (6 units available)
https://www.ebay.de/itm/123873406755Perhaps ask the seller about the exact size of the part. IMO, they seem a bit too short (perhaps only 35 mm travel, 50 mm full lenght).
Most of the PREH faders I could find are
upright models 
Those in the VES TWO are of flat shape and are actually lying. But ask Greider if they dont have a few parts that matches your requirement.
Furthermore, the part you describe has a 50 mm travel, and this is unfortunately rather uncommon. Standard travel course are 45 mm and 60 mm.
Also check the other defective fader if they are exactely the same as the one you already dessoldered.
Do you want only a genuine replacement part ? Or would a functional replacement suit too ? In the latter case, adapating another fader having similar mechanical size would certainly be possible and do the job.
If a functional replacement is acceptable, the important features are :
- the fader height
- the fader
resitive law As nothing is indicated on your fader, I would assume it is 'A' (linear), but this has to be verified
- the fader total lenght (because too long might be a problem if other parts are located in vicinity.
- the fader mechanical travel distance, but it's possible to cheat : 45 mm might do it, and 60 mm too, but in this case, it needs other cobblings to work properly (I we need too go that way, i'll be more specific in a later post)
What is NOT important :
- the fader total resistance value : as far as what you need is an 'A' law, the actual resistance value of the replacement part can be equal or above 10 k (because it's always possible to add a parallel fixed resistor so that it behaves as a 10 k fader)
- the actual position of the pins (electrical connexions to the resistive track or the mecanical positioning pins), because it's always possible to drill new holes in the PCB and glue the fader at its' adequate position
- mono or stereo fader : if you catch a stereo fader, just use one side.
Some interesting parts that might be an acceptable replacement :
10 k (unknown law) 45 mm
https://www.amazon.fr/lin%C3%A9airement-Potentiom%C3%A8tre-coulissant-coulissante-potentiom%C3%A8tre/dp/B07D42SYPH10 k A 75 mm total lenght
https://fr.aliexpress.com/item/32990553553.html10 k A 60 mm travel
https://sinolec.co.uk/en/slide-potentiometers/1211634-10k-ohm-slide-linear-slide-potentiometer-fader-with-dust-cover.html