NOT A TEACHER
(1) For easier analysis, may I simplify your sentence? Let's delete (erase) the adjective (relative) clause. So we have two sentences:
(a) The beggar turned out to be innocent.
(b) The beggar turned out innocent.
(2) I found an interesting article on the Web taken from the Oxford Advanced Learners Dictionary:
(a) The job turned out to be harder than we thought. "Turn out to be" = to prove to be.
(b) If the day turns out wet, we may have to change our plans. = "Turn out" = to develop or end in a particular way.
(3) Therefore, it is only my opinion that it might be better to say:
The beggar whom we had suspected to be guilty turned out to be innocent.
EDIT: Many thanks to the moderator for pointing out my mistake.
Student or Learner