Which master socket do you have as you could connect the particular extension wiring assuming it is directly wired to master by connecting the wires to the data terminals in master
you could also use poweline adapters and leave router where it is
Like one f these
did you consider powerline adapters which would be easier?
Just move the 2 wires from the extension that are connected to terminals 2&5 on the removable faceplate of the master to the data extension terminals shown by the yellow arrow in the picture.