Again it would be very difficult but there's more chance with the LG one. Changing 5V to 12V will be difficult though, you are asking it to produce more than twice the voltage it's supposed to give. To be honest, it wuld be less expensive and far easier to buy a 12V adapter and forget this project completely. Also bear in mind that you won't get any more power out of it, trading 5V for 12V will also reduce the possible output current from 1 Amp down to about 0.3 Amps.
If you want to try, you have to replace the two capacitors in the top right corner of the middle picture with the same values but at least 16V rating, they will be larger than the existing capacitors so check there is space when you buy them.
Then you have to adjust the feedback circuit by changing some resistor values, I can't see the tracks clearly enough to tell which ones but they will be in the area around R15 to R23 in the top corner of the third picture. Without a schematic I can't tell what values you need though.
Again - beware of lethal voltages! don't be fooled by it being a small adapter, it will have voltages probably > 300V in it.
Brian.