To make a replica PCB, you need to know where all the copper-traces connect to. For the bottom side, this is not so difficult, you only need to remember to draw the mirror image in a PCB drawing program. I measured all the locations of the holes and via's and drew them in the PCB drawing program. After that, I connected all the copper-traces to the holes and via's.
The upper-side of the PCB is more difficult, because the components are obscuring the copper-traces. You can use a multi-meter and measure all the connections, but that is not that easy and can lead to mistakes if the components themselves connect different holes internally. For that reason, I removed all the components from the upper-side of the PCB.
The replica PCB is very close to the original, but there are some small differences. The PCB drawings are made with EasyEDA, which is a free online PCB development program.