Pairing up Mesa 7i76e with VFD Delta C2000

I did some more research being helped by a friend that's more into electronics.
We have discovered that the board outputs differential outputs, and there is no common ground between the phases.
Also we discovered that the voltage is from -7.5 to +7.5 and not from 0 to 15
We created a voltage divider using two 500ohm resistors, and filtered the noise with a 1nF capacitor. We ended up with a 4.8v peak to peak.
But this voltage is from -2.4 to +2.4 and not from 0-4.8v.
Can I feed this signal into the mesa board? Or do I need a 0-5v signal.

So you're saying its ok to feed into the mesa board a signal that' from - to + and not from 0 to +?
I would not like to get my board fried.
I thought I need to supply a signal between 0 and 5V

7I76E differential encoder inputs have a common mode range of -7 to +12V
and a differential sensitivity of 200 mV, and a maximum differential voltage of 5V,
So the will take positive and negative inputs as long as they are in that range

You must make sure that no input exceeds +13V or -9V or you may damage the input receiver chip. If you have large signals and large noise spikes, you should use your input divider. Note that the 7I76E encoder inputs are terminated with a 120 Ohm resistor across the differential inputs pairs, so you may need to adjust your divider accordingly. As long as you get about 2V across the inputs its good.

I have made today some measurements and some tests. I have discovered that the encoder board has a SG pin that I assumed it comes from 'signal ground'.
I have connected the ground of the probes to the ground, and then connected the probes to the A and A' with a 110ohm resistor between them to simulate the internal resistor that mesa has.
See the measurements in the pics below.
I am wondering if the noise that appears in the signal can get out of the -7/+12v range and if this could affect the mesa board.
Given how the signal looks now, do you think its safe to connect the wires to the Mesa's encoder input?
Also, do I need to connect the ground from the encoder to the GND encoder pin on the Mesa?

Do you think a double shielded FTP cable would do it?
You said about connecting only one side; here the sides I have are the Mesa board and this board that converts from the resolver signal.
To which of them should I connect the shielding? Where should I connect the shielding? To ground?
Sorry if I'm asking stupid questions, I'm a very beginner with the electronics.

I have replaced the cable with a double shielded S/FTP cable.
Now the signal is more clear, it has some spikes and the VPP is 8v so between the -7v..+12v range. The base is 300mV and the top is 3.6v
Between the A and A' I have added a 110ohm resistor to simulate the internal resistor of the mesa board.
I assume its safe to connect now the encoder to the mesa board.
So my encoder has differential outputs, so I will have 6 wires for A,A' B,B' Z,Z' and GND.
Is it ok to connect the ground of the encoder to the ground on the encoder port on the mesa?