Why is 他 put after 出 in 认出他来 in 女大夫很快认出他来? In the following sentence:


  他正往楼上走，徐廖正碰见那位女大夫。女大夫很快认出他来。就这样，他被扭送到派出所。


I wonder why 他 is put after 出. 认 is a verb consisted of the single word, not 离散动词. (If it is 离散动词, 他 should be put between them, right?)

All the sentence I have seen puts 他 before 出, IIRC. So the sentence is 大夫很快认他出来。

So my questions are:


Why is 他 put after 出, not before it, and it is grammartically correct? Or is 认他出来 grammartically NOT correct? 
If there is a difference between the two pattern, what is the difference? Or are they just synonysm?
认 (recognize/identify) is the verb and  出 is its result complement 

认 = to recognize

认出 = to recognize (and success)

We cannot insert the object between a verb and its result complement

Examples:


We cannot insert the object between '看见' and say '看(他)见' , we can only say '看见(他)'
we cannot insert the object between '听到' and say '听(声音)到' , we can only say '听到(声音)'
we cannot insert the object between '认出' and say '认(他)出' , we can only say '认出(他)'


I think the confusion come from the presence of '来' at the end 

If it was just '女大夫很快(认出他)', we can clearly see '女大夫很快(认他出)' is grammatically incorrect

But in '女大夫很快(认出他来)' '认' would be a single character verb and 出来(out) would be a preposition (away from inside)


[认][他][出来] = [verb] + [object] +[preposition (out)] which would be grammatically correct -- That's why you think '他' should be placed before '出', but the fact is, 他 could only be placed before '出来' , not '出' (see example #3 above) 
[认出他][来] = [verb + result complement+ object] + [final particle 来 (indicates an outcome)] which would also be grammatically correct - It is what we see in the sentence in question


More examples of  出来 as a preposition (out):

推(出来) = push (out)

拉(出来) = pull (out)

For the above two examples, you have to insert the object between the verb and 出来, as in "推(他)出来" = "push (him) out" ; "拉(他)出来" = "push (him) out"