Today while installing the fibered laser in DAQ room instead of the pick-off from the injection we realized that the input fiber connector of the splitter box was actually broken inside.
This explains why there was more losses than expected between the 35 mW at the output of the fiber in DAQ room and the 7-8 mW at the input of both telecom fibers.
We replaced the faulty connector (and also the others) and measured about 15 mW instead of the 7-8 mW.
When plugging back the fiber from the injection, we will have to tune the gain of the SOA in order to adapt to this power.