I assume the standard sketch where : SoftwareSerial softSerial(2, 3); //RX, TX
As such RX and TX looks to be switched. Try
M7E RX to UNO_R3 pin 3
M7E TX to UNO_R3 pin 2
GND to UNO_R3 GND
VCC to UNO_R3 5V
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