Bricked Mesa 7i92T

Please tell me, can I use encoders from the Mitutoyo AT111-100F або AT111-200S series?

I don't think so, those appear to have analog sinusoidal outputs so
require an interpolator (that is, they are not standard quadrature encoders)

Is it impossible to convert the signal? If it is possible, how?

You would need to know the signals levels.
Do you have a full data sheet?

It might work with the common Heidenhain "EXE" boxes 
which are sine/cosine interpolators with digital quadrature outputs

No, unfortunately, I don't know anything about that. I bought a non-working machine with these rulers installed on it. In order not to buy others and save money, I thought that maybe I could use them.

That's what GPT chat told me.)))))))

Does the machine not already have the interpolators built in?

IC Haus makes analog interpolators :

ichauschina.com/en/products/interpolator.htm?productid=2