@evangelosem5125 I would have to second Alisha's opinion that if this was something you wanted to try and fix yourself, then the battery is the place to start. They've already given you a link to the guide you would need in order to do the repair yourself.
Be aware that Apple has started pairing the battery with the logic board on your phone, so there would be a couple of consequences you would encounter should you do that repair. First, you'll get a warning to the effect that the battery may not be a genuine Apple part - even if you use a genuine Apple battery. That warning will pop up when you power on the phone for a week or so, then it'll go away. However, there will be a permanent badge on your Settings icon and a warning to that effect within the Battery section of your Settings.
Secondly, whenever the non-genuine warning shows up, Apple disables your ability to view the battery health information. You'll still be able to see how much charge it currently has, but the maximum capacity information will no longer be available.
There are ways around the issue, but they involve salvaging the existing Battery Management System (BMS) circuit board from the old battery and transplanting it (including soldering and/or spot welding) onto a new battery cell. In your case I would advise against that approach, since it appears the BMS may be suspect in the charging issue you have. You could go to all the trouble of transplanting it only to find that you've also transplanted the problem along with it!
The battery health information you retrieved from the phone (87%) says the battery isn't in horrible shape, but it is getting close to the point where it would be recommended to replace it. Any reputable repair shop can do the job, but be prepared for the consequences I mentioned, unless they're an Apple authorized repair center then they won't be able to pair the replacement battery. Unfortunately, Apple's self repair program didn't start till the iPhone 12, so you're out of luck in that department.
Should you decide to go ahead and replace the battery, there's a possibility the problem may still be there, as Alisha mentioned, part of the charging circuitry is in the lightning port flex cable assembly so the issue could be there. I'd hang onto the battery just in case. Anyway, if replacing the battery doesn't fix the issue, the next step would be the charging port assembly. Here's the iFixit guide to that repair.
[guide|129075|iPhone 11 Pro Lightning Connector Assembly Replacement - iFixit Repair Guide|new_window=true]
Note that this guide is not authored by iFixit, and is a video guide only; it doesn't have the step by step written instructions like the battery guide. If you prefer the written guide, there is an excellent one done by the website Nadie Me Llama Gallina. Note that it's written in Spanish, but if you use it with the Chrome browser's translation, it works quite well.
[link|https://www.nadiemellamagallina.com/en/manuales/smartphones-1/apple-5/apple-iphone-11-pro-1153/placa-auxiliar-10215|Manuales / Apple iPhone 11 Pro / Auxiliary board - Nadie Me Llama Gallina|new_window=true]
Between the two of us, Alisha and myself, I think you have all of the information you need to make an informed decision on what you want to do with your son's phone. Good luck and let us know how it all turns out!