I done this back strap based on how i do my tomahawk steaks on a kettle bbq.
recommend a good understanding of how you use your type of smoker
good set of probes.

First i Started with 15 Ashed over coals and added them to bqq to pre heat.
Adjusted vents to hold internal temp[ around 100 degrees celcius
Add smoking wood

Add Backstrap with temp probes

start another chimney of coals to be ready for sear

cook until 52 degrees C internal. ( medium rare )
you can change this based on prefrence
rough time is 40 to 60mins
can vary but internal temp is key.

remove and rest in foil

Add new chimney of hot coals to bbq

Get BBQ to around 250 to 300 Degress C

Return Backstrap and sear each side for a 90 seconds.

remove, slice and serve.

:note, there is still a heap of usable coals so cook something else if you can to store for later or weeks meal prep.