Combined, these look awesome! The egg shape is very unusual and the FILLSTA base makes it look like some sort of spaceship.
The LED lamp used to work very well. It had an inductive charging base so it was possible to remove the egg completely and have it running on batteries for a while. After some time however it wasn't as bright any more so wasn't really usable. Its disassembly was easy, just a bunch of screws holding the LED portion together. Unfortunately the LED part of the lamp couldn't be disassembled as it was fused together plastic parts with circuitry inside. I guess they didn't want anyone to be able to fix it!
The FILLSTA base was just a standard E27 socket lamp base that connected to mains and had an on/off switch. I had an RGB light bulb that fit this socket and as a bonus the light bulb had its own remote control.
So all I had to do was combine the egg and the base...
My mere luck the FILLSTA base was almost the exact dimensions of the original (faulty) LED part that I removed from the egg. All I had to do was enlarge some of the holes on the base so that the original screws could be used. I ended up using just three screws - it wasn't coming apart at this point so I didn't see the need to add more.
That was it! Really quite a simple project. It only took a few minutes to actually put together once I got started. Now I have a cool looking new bedside lamp!