I have two audio tracks of dialogue: First, the speech of the client, second, the speech of the manager. The recording was done with two microphones. Unfortunately, each track contains the little sound of each other (for example the audio with client contains the soft voice of manager). How I can сlearly separate this audio?
What you are describing is called 'spill'. It is a very usual problem in recordings - especially drum sets where you have many sources and many microphones close together.
The most common solution is the use of a noise gate.
Since they speak at different times and because of distance one sounds more quiet than the other, I would set the threshold level just above the level of the quiet speaker on each mic track.
This should mute the sound when the speaker that is meant to be recorded isn't speaking.
I assume the whole recording is quite long. Otherwise you could just edit those bits out yourself. The advantage of the gate is that it will cut them automatically but you will have to hear the whole thing to spot any bits it might miss because the lower voice became a bit louder and triggered the gate open.
If you can spot the most problematic part and use that to set your threshold level it should be ok.