Trouble using the KellerModbus library

That's strange. You can have several devices on an RS485 bus. You could try removing the terminating resistors on the click board - I think that's controlled by jumpers on the click board, so no butchering of the board required.

I can't, if I do so the Keller Software is not receiving data

Here is the actual wiring

If you remove J2, J3 & J4 on the click board, then the PC software stops communicating with the sensor? With the click board in permanent Rx mode and the jumpers removed, then the PC should communicate with the sensor as if the Arduino wasn't there.

It's not quite that. The same issue happen even if J2 J3 and J4 are removed or on the click board : as soon as I plug the 5V supply from the click board, I get no response from the sensor.
I can clearly visualize it on the scope : The PC software made its requests but get no answers. The click board must not be powered in order to get response from the sensor... This made no sense !

I've checked the behavior of the click board when it's powered and when it's not. The DEREpin is still at a LOW level when powered, and there is no transmission from the Arduino (as the sketch is only listening).
Speaking of the sketch listening , here are the data is he's sniffing :

It should be at least a modbus frame requesting the data but it's not...

This is a correct request frame from the keller software captured with the scope :

and this is the only frame I get when the Click board is being powered. I assume it's the request from the Keller Software since the Arduino sketch is not emitting :

judging by the size of the frame, they are clearly not the same.
So I don't understand why when my click board is connected the Keller software is not emitting the correct request...

Thank's for your patience all

I'm at a loss as to why this isn't working for you. I had a look at the ADM485 datasheet just in case it was something really silly like their RE & DE signals were the opposite of the standard MAX485 chips. It wasn't that so I too don't understand why adding a listening device to the RS485 bus results in the sensor not responding.

for what's worth I think that ground wire conneting the USB-RS485 converter to the arduino sheild should not be there.
Given all the stuff that have been tried (KUDOs to OP) might as well as try removing it and see it if the SENSOR, PC interface start working again with the arduino also connected/powered....