Battery stuck at 1% after replacement, however shows 100%

Hello.

Recently got an iPhone 5s in my hands with a really weak battery so decided to replace it and give the phone another life.

After the replacement battery is stuck at 1% and after few seconds of use the phone would turn off. At the same time if I connect it to power source the battery jumps straight to 100% and stays even if I disconnect the cable but would turn off anyway after some seconds. Like the phone thinks that battery is full but actually it isn’t (or maybe it is?). Seems to be warming up while connected to charger so I suppose actually it is charging? Reattached all the cables, tried DFU restore - didn’t help (weird that the phone would go off even with the cable after some time, but it won’t turn off during restore), tried to charge it overnight while turned off, but at the morning it was still on 1%.

Could it be faulty U2 Tristar charging IC or maybe someone have other ideas?