It's time to release your anger ! 

Open the old battery (I had screws). ACT WITH CARE : the battery, even weak, has some energy left and could arc with a watch, ring, bracelet ... and burn you.

Fit test :

Hack it up! : 

I cut the edges keeping the electrical connector interface.

In my case the connector was soldered to the board (the black piece on the PCB), so I de-soldered the board from the cells and then de-soldered the connector from the board's underside :

Glue the connector to the case and solder wires ;

We are done here ! Next comes the assembly.