In most cases, I _totally_ agree with PawPaw. If you want to take an entirely new LED and add it to a
device, he and Belle are absolutely on the right track. You will absolutely destroy a few until you learn the handling of SMT.
BUT
If you want to swap two, one from the other, it's actually pretty "easy" by comparison. The LED board (on my autos, anyway) is an entirely separate board. You could CAREFULLY clip the wires leading to the battery one side and the MCU on the other, move them over, and carefully splice in a small extension wire (#24-26 gauge insulated wire-wrap wire will work. ) You'd need to solder that extension into place, then solder that to the original wire to the MCU and battery (the battery side doesn't really need an extension, it can be spliced in place if you're careful and your cutters are sharp). You need to work quickly with the iron and with purpose to keep from destroying the LED, the MCU, or burning the insulation. Once you've done that you need to insulate the wire splices. Or if you can find some fine enough heat-shrink tubing, do it before you make the splice, on the long side of the wire.
280deg for ~3sec should be safe enough on either
device. You'll need low-temp solder.
It's been a long day, and that's probably a pretty inadequate description, but if you already have the skills, that should explain it well enough. Check my high-res close-up photos and it should be clearer, especially the assembled unit - less case.