The original circuit shows a 10uF capacitor between pins 6 and 7,
This can best be described as odd, I guess that the guy who drew that circuit intended to write 10pF.
Looking at the SA602 datasheet, we find various options for an oscillator:
Here, the writers of the datasheet (NXP Semiconductors) are showing how to connect the SA602 oscillator section to a synthesiser by tapping the signal at pin 7 of the SA602.
They also show a few options for buffer amplifiers to to prevent the synth from loading the oscillator circuit.
If the connection from pin 7 to your counter input is a short distance, it may be worth trying a direct connection, but be prepared for excessive loading and frequency shift when the counter is connected. In which case built one of the buffer circuits close to the oscillator and run a longer screened cable to the counter input.
But above all, don't forget to check that C11 on the receiver board is more like 10pF that 10uF.
JimB
PS, it looks like RonSimpson and I read the same datasheets!