iPhone X with 56% battery health

If you do not have a problem with how long you can use your phone from a 100% charge, then don't worry about it. Usually you will want to replace the battery when the health falls below 80% and it is noticeable by shorter usage time and restarts that limits the batteries peak capability. No one here will recommend getting a non-Apple battery from an unauthorized service center and that could be the reason why you are seeing those results.

When the time comes that you are seeing poor usage time or limits in the Peak Performance as noted in the Battery settings, then get it replaced at an authorized Apple service center using genuine Apple parts. That is the only way you would know if your phone is living up to its potential. It is only $89 to have the battery replaced by Apple in the US.

Buying any used Apple device is always risky. Please see this excellent User Tip submitted by one of our most respected contributors:

The All Too Common SAD Reality of Buying … - Apple Community

If I to install a genuine apple battery in an Apple store will this restore the battery health to 100%?

No one here can address that. We cannot test your phone. However, be very aware that Apple make elect NOT to work on an device that has been serviced by other than them or an Apple Authorized Service Provider.

I think you should return the phone for a full refund based on the fact that the seller cannot make it right.

meirlroy wrote:

 "No one here will recommend getting a non-Apple battery from an unauthorized service"

thx man. I know all the restrictions of replying on a web site like here.

I will go on with my current battery until I'll have to replace. thx

I meant no shame or disregard by my comment. You asked:

"The man in the shop replaced 3 new (not genuine) batteries for testing.

The result was the same. 56% health.

The batteries are new and they can't be the cause of this low health %

So where is the problem? "

There is no one here that can answer that and obviously the repair person had no answer for you either. The point was that the only way you could get that answer is by the genuine parts serviced by Apple. If there was a problem, they would have an answer for you.

The algorithm Apple uses to determine battery health could easily show a non-genuine battery as having a lower Health %. The specs of the battery may not even be the same. It's no different than comparing a store brand AA battery to a Duracell battery. Even though the voltage may be the same, you will not get the same results.

I even made a point in the first sentence of my comment that if you are happy with the battery life, then don't worry about getting it replaced.

It is my understanding that unless the battery is replaced with an OEM battery by a certified technician, Battery Health will either not show at all or not be accurate.