shifter/derailuer compatability

I’m sure it works, but am doubting myself so am asking before ordering.

Shimano 9spd bar end shifters - SL-BS77
with 9spd XT shadow RD-M772

Hoping that the indexing will work on the rear, and the front will have enough throw for same series crank?

Can anyone comfirm this for me?

yes it will work.

I ran 9spd bar ends with a deore external BB triple crank and a 9spd (older) XT rear derailleur.

All shimano 9spd parts are interchangeable/compatible.

Fine. made to work together.

Barcons have enough pull for triple mechs.

Awesome, thanks for the quick replies.