A minor upgrade to my transmitter.
I increased the voltage to the TTL crystal due to the resistance of the modulation transformer winding.
I also added a resistive feedback from the crystal output to ground, which resulted in the negative part of the PWM signal also being modulated.
After that I put a coil that converts PWM to sine wave, followed by an RC circuit for little impedance matching and a transformer that reduces the output impedance and smooths the output signal.(PWM is a rather poor signal for transmission, it is more difficult to work with and has a lot of harmonics.)

And then I connected the transformer output, to the second board, and it's magic.
The coax I used to connect it should have an estimated capacity of 5pF and reduces the output impedance from 43Kohm to 15Kohm, so it will be more convenient for the next stages. (because it adds a capacitive reactance of 32 kohms)

So now I have 2.2Vpp at the output at a load of 15kohm.
(I measured with a 100k potentiometer, taking care to remain in the linear range without distortion or significant voltage drop).

I also added an amplifier module with TDA2030 to amplify the signal going to the modulation transformer.
And I was pleasantly surprised that it is capable of supplying sufficient current even with relatively high amplification, because it works both as a microphone preamplifier and as a driver for a 20-ohm modulation transformer winding