Thank you for taking the time to read my post :).
The stm32f4 sends at most 3 volts for an output high, the 5 volts arduino uno needs at least 3 volts so I thought I need a conversion from the 3 volts to the 5 volts:
stm32f4 TX sends 3v --> logic level shifter --> arduino uno RX receives 5v.
Of course you don't have to read the reference, ask me anything about the stm32f4 and I'll look for the answer in the reference.
stm32f4 ------> stm32f4 OK
arduino uno ------> arduino uno OK
stm32f4 ------> arduino uno KO
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when the stm32f4 sends a character the arduino receives two!
example : stm32f4 sends A the arduino receives äÿ -
when the arduino sends a charcter the stm32f4 receives one.
example : arduino sends A the stm32f4 receives þ.