3rd party iphone screen, will Apple replace my battery?

My iPhone won't charge, it recognizes that there's power as the charging icon comes up, however, my phone won't store the battery. I have been advised to send it to Apple, however, my screen has been replaced by a 3rd party company, therefore it is not an Apple screen. Does anyone know if Apple will replace my battery? I'm happy to pay the cost as I know my warranty is invalid, but will they fix it for me?

Sure. But not for free. You have to pay for it.

As long as you're paying then Apple don't care. Note that if you're in the USA then only the part of the warranty relating to the screen or any faults directly arising from use of 3rd Party parts will be invalidated.

But the fault you describe is a classic description of a very common fault: a failed charging cable. Lightning cables used from the iPhone 5 onwards are notorious for it, and the cable fails just enough that the phone recognises it's been connected to a charger but won't actually charge.

So before you try anything else, try another Lightning cable. The ones which fail during AppleCare get replaced free as many times as they fail but I have heard of others being replaced out of warranty without any further questions. The earlier Thunderbolt cables with a Lightning adapter seem to be far more robust. The Lightning cable design has been changed at least once but I'm now on my fourth since getting my iPhone 6 last December, and friends also have had experience of them failing in exactly the same way without warning at just three to four months.

They will fix it the battery, but as you stated, you will have to pay more since your warranty is void.

Lol pay 200+ just for battery replacement buy the battery your self go to some phone repair and they will go under 10$