- a) checked by him. (correct)
I'll have all the locks checked by him.
You are specifying that you'll let him to check all the locks.
- b) be checked by him (correct)
I'll have all the locks be checked by him. (Incorrect)
Now, specifiying that all the locks to be checked by him. Note: Nobody will let him to check. There is a passive voice because you specified that all the locks to be checked by him. I'd prefer don't use any subject for this sentence.
All the locks will be checked by him.
- c) to be checked by him (incorrect)
Unfortunalety, that's incorrect to use with any subject.
If you use ''To + Be + Verb + ED/ V2 / V3'' as i mean Passive Voice, it couldn't be subject of the sentence. Because the verb you specified will be object of your sentence.
So you only can use
a) checked by him
Hope that my answer see work!