Mark completed Russian author via audiobook (5,3)
I believe the answer is:
check off
'mark' is the definition.
(synonyms)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for check off that I've seen before include "Tick names on list" , "Record correct" , "Maybe put a tick against" , "mark listed items systematically" .)