Dear Shannon , I have already connected the GND of the Modem and GND of the Mayfly. Interfacing between Mega2560 to the Modem I have used of level converter ( 3.3V to 5 V) for TX1 and RX1 . Because the operating of the modem is 3.3 Volt and the the Mega is a 5 Volt.
The operating of the Modem was a 3.3 Volt for the RX1 and TX1 and operating the mayfly also 3.3 Volt , so I connected directly without level converter. With this wire , modem still could not communicate with the mayfly. whether the communication function is not due to the difference in speed? Just information the baud rate modem fix 115600 bps and the mayfly 57600 bps.