Is there a limit on how much more ampers can I supply for a laptop?

My laptop uses a charger outputting 6.4A with 19V (120W). This charger was a replacement for the old one, the specs were almost completely matching (19.5V and 6.15A on the old charger), everything works perfectly.

There is, however, another laptop, which doesn't see the charger when working and barely charges with the 20V and 2A of the AC adapter, which is 40W. It sounded like a clear indication of not enough Amps, so I checked that the voltage and connector were (almost) matching and tried it with my adapter (3 times more powerful), and it worked perfectly.

I have heard before that it is completely safe to bring more Amps, because amperage is pulled, not pushed, so I believed the experiment to be safe, and was going to buy the same charger for the laptop's owner -- but she has also asked her brother, and her brother told that it is not safe to change amperage by more than 2A, some googling revealed the same statement about 1.5A. So I would need to find out the original amperage and choose a charger carefully.

So: Is it completely safe to use a charger with considerably bigger amperage if other specs, including polarity and connector shape, are matching? Is there any limit to this?

Answer

You are correct, it is completely safe to use a charger with a higher amp rating. Her brother does not understand basic electronics.

The electronics formula is quite simple: Voltage=Current * Resistance.
Therefore Current=Voltage/Resistance.

The voltage is fixed, and the resistance varies depending on the exact paths the power takes to feed the components of the computer - thus the current drawn varies DEPENDING ON THE PARTS IN THE COMPUTER - not the power supply.

There are - as you appear to be aware - an instance where this is not true - where the available current is less then what is desired - in which case the voltage would drop (assuming there is no protection circuitry). If - hypothetically - the manufacturer were to design the computer to expect a lower voltage because of the current drop by drawing too much current, then your brother would be correct - however this design choice would be insane, because it means building a system that is dangerous and designed to fail in a dangerous way, and there is no advantage to it (even if the manufacturer wants the system to eventually fail, there are safer ways to accomplish this - without exposing them to the same unquantifiable liability)