I made the profile of the pump, the HeNe and the 1310nm laser.
I used the blade on the translation stage to cut the beam and measured the transmitted power with the power meter connected to the labview software that makes scans. Then I fitted each scan with the erf function and then I fitted the profile for each laser beam.
The blade 0mm position is at 75mm from the optical board, and at 172mm from the mount of the last focusing lens of the pump.
I upload the previous measurements of the profiles (first 2 plots) and the new one (third plot), after replacing the 1310nm laser. After changing the fiber, the waist size didn't change but the waist position moved a few cm.