Can I charge my HP Probook 430 G5 from 2018 with my Galaxy S10+ USB-C Adapter

I need to charge my Laptop but I don't have my normal charger here, so I've done some research about charging possibilities and found out that my Laptop has a USB-C Port which is also a second possibility to charge (found that Information on the HP Website).

But this so called usb-c port on my laptop looks a little bit edgier than my Samsung usb-c charging cable. It fits into the port without any problems and I can also see that my laptop works with the received signal from my cable (everytime just for a short moment / 3 seconds), but it doesn't seem to charge and the battery goes also down. Maybe I need a better usb-c cable? I want to buy the HP 3PN48AA Universal, but before I buy anything I need to know if its even possible. Thank you in advance.

The S10 charger is probably limited to 9V and 1.7amps of current, probably putting out 15 watts of power. It might even be able to give 25 watts. (A little above 2.5 amps). It is intended to charge a phone with a small 3.7V battery.

Your laptop probably expects either 12V, 15V, or 20V in order to charge. It has a much larger set of batteries to charge and requires a higher voltage in order to drive current into the battery cells.

USB C Power Delivery may mean we now have a single connector and cable to charge things but it does mean we also need chargers capable of meeting the demands of the devices attached. A laptop USB C charger may well be able to put out up to 100watts of power (20v at 5A) while a phone charger has almost no need to supply that much.

USB PD chargers can be selective about what voltages and currents they support. This can save a lot of expensive components for devices intended to only charge phones.

Mobile phone charger: 5V, 9V, 10V (Samsung)
Laptop USB C charger: 5V, 9V, 12V, 15V, 20V

USB PD starts a connection at the standard 5V (to allow basic electronics to work) and then allows the two devices to negotiate supported voltages, if neither device supports a common required voltage level then they will simply stay at 5V. For a phone that may mean slow charging, for a laptop it will mean no charging.

If a laptop battery has multiple cells then it may well operate at 7.2V or 14.4V, the voltage from your charger needs to be higher than that voltage. Hence many high powered laptops need either a 15V or 20V charger. Otherwise the laptop needs extra charging circuitry to "boost" the voltage up to a good level and draw more current to compensate. That is extra cost and most manufacturers will simply say "use the manufacturer supplied charger" which puts out the correct voltage and leave it at that.

Even if you have a 7.2V battery a 9V charger may only be able to put out 1.5-2A of current. Depending on the size of the battery this may result in a charging time that is excessive of the order or 4 or more hours. Increasing the current will result in more heat generated in wires and could be a hazard. Increased voltage on the other hand (20V instead of 9V) would reduce heat at the wiring and connectors at the cost of a slight increase in conversion loss inside the device which would be handled by the cooling there.

While you should be able to charge your phone using a laptop charger, even if slowly at 5V, you won't be able to charge your laptop using a phone charger.

There are many hits on Google that suggest that USB charging will work on your device.