I completed the assignment today. Went to another system but in the same state (screenshot with same system type, I were in LP 532-81):
First I tried
Akpabio Agricultural Holdings and it did not have any power lockers at all. So I chose by random
Kobyliansky Chemical Enterprise. In my first attempt, I opened both lockers, got some loot, went back to Archer's system, offload it. Second attempt, I opened first (easy) locker, grabbed items, went to offload, but turned out I still need one item more. I went back to
Kobyliansky in third time, opened 1st locker and it was empty:
To repeat myself, I went to another system, returned back and locker is empty. I opened 2nd locker (it was harder because of guards) and there were 2 power items inside.