When engaging transmission the vehicle starts to shut off

Does it smooth out if you hold the accelerator pedal down a little? If the engine runs normally at all other times, the Engine Computer may need to relearn "minimum throttle" before it will know when it must be in control of idle speed. That is required after the battery is run dead or is disconnected.

To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals.