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@EdgarBonet Not what I meant. I know the resistor is not that long and meant adding it between the connection TX and RX. Your EDIT is clearer and it makes sense it adding the resistor to the sending side.
Not sure what you mean as "resistor in series with the TX pin". You mean a resistor from TX pin(Arduino 1 ) to RX pin(Arduino 2). A little image with the drawing would be helpful...
