Take the new 0402 fuse with a pair of tweezers and solder it back in a similar manner to the removal of the old fuse.

If you do not have or want to use a fuse you can simply bridge the 2 contact points and it will work the same without issues. But it is better to be on the safer side by replacing it.

At this point you should use a multimeter on any of the capacitors present to check for a short/continuity. If you do not hear anything, then you can plug the charger in, and the white light should reappear, with the charger working well.

If you have plugged the charger in without checking for continuity, you will get a yellow/red/orange led, with the charging chip heating up, which means that there is a short on one of the capacitors. That's why I recommend first to check the continuity.

The second image has 2 red rectangles, any one of those capaciors could be burnt out. So what you have to do is remove them 1 by 1, until the short disappears, always checking with the multimeter. In my case, 1 charger was the fuse, one was that with the decoupling ceramic capacitor near the fuse (the black one). A 0.1uF 0603 SMD will do just fine.