iPhone 5S says it charges, but the battery percentage is not increasing

An iPhone 5S that says it is charging, but is not! All the bells and whistles for charging is on. As soon as the original Apple USB cable is connected, the iPhone goes "ping!” the screen turns on and shows the "Charging" and current battery percentage. The little lightning in the upper right corner is also present and everything indicates that it is charging. However, it is not increasing the battery percentage at all! The first part of the video (up till 0:30) shows another iPhone 5S used as a reference phone, to just show you that the cable is OK. All other iPhones and iPads in the household charges fine with this cable! At 0:57 you will see that the reference iPhone has gained 2 percent in Battery charge in just a couple of minutes. At 1:41 we switch iPhones, and now the faulty iPhone 5S acts the same way as the reference iPhone, and indicates that it is charging all the way. The battery percentage at this time is 2 percent. At 1:41, approximately 10 minutes later, we see that the battery percentage is still 2 percent. The challenge is that it does not behave like this all the time! In a week, it can suddenly charge up to 13 percent one night, and up to for example 57 percent another night. It might EVEN get to a 100 percent once in a while! The problem is of course that you cannot "trust" the phone to be charged overnight, and thus render it useless that day! Another problem is that Apple has already serviced this iPhone once, but "according to their test procedures" could not find any problems. I guess they were just lucky to have it one of those days it actually did charge somewhat. I however would however guess that it would be difficult to get it to charge up to 100 percent twice over two days!