Apologies for not having more detailed images... I don't have a good setup for photography while using both hands.

If you have trouble with this method, you may have better luck by removing as much solder as possible using solder wick and a solder sucker before pulling the microswitch away. However you do it, all three terminals will need to be warm enough to melt their solder at the same time.

Double check to make sure each solder pad on the bottom of the circuit board has continuity to the trace surrounding its corresponding hole on the top of the circuit board in case you separated them while extracting the old switch.