E70 3.0 Diesel starting problems

[Chris92]

Greetings!
E70 3.0D 173KW M57 2008

I've searched on google for days and I can't find the exact same problem as I am experiencing

A cold car starts without any problems. When it has already warmed up, after turning it off to go into the store etc., it is problematic to start it back up again.
It shows the error on Idrive "Fuel Pump Faulty. Engine may stall".

When connecting to the computer, I see one error "No message from EKP (electric fuel pump) controller unit, receiver combi, transmitter EKP".
The EKPM, or electric fuel pump control unit, has been replaced. Immobilizer and remote control batteries have been replaced. The problem continues.

As far as I understand, the problem is communication, not pump operation.
The serviceman recommends changing the electric pump and fuel filter, but as I mentioned, a cold car starts and drives without problems, enough power, no smoke, etc. If the electric pump overheats, then the EKPM reduces the power after entering the safety mode, I did not observe anything like that for mine.

It's not every day either. For example, this week I drove for 2 days without any problems, starting, turning off several times in a warm car. The fuel level in the tank does not affect it in any way, a full tank has also been tried, so it will not be a transfer pump fault on the other side of the tank.

I can't find the EKPM electrical diagram for my car, maybe someone has had the same problem?