but tutorial given only using UART connection is using serial monitor to move the stepper motor.
The sample sketch is using the serial port to control the motor. No Serial Monitor is involved in the process.
If you don't want to use the hardware serial port (pins 0 and 1), use some other pins and SoftwareSerial (or NewSoftSerial for 0023 and earlier).
my project have to use the lcd keypad shield to control the stepper motor speed.
So, the keypad will be used to collect the speed data, and the serial port (hardware or software) will be used to convey that information to the motor controller.
any other method how to connect arduino with enhanced 2A stepper motor driver?
Duct tape? Twine? Hot melt glue?