Turning 2 phones into 1-OK to just replace logic board not all?

I have 2 Iphone 4s': A black non-working iPhone 4S in perfect physical condition, and a white cracked-screen-but-working iPhone 4s. I want to put the white phone's guts into the black phone's shell (covers). I have followed the "screen replacement" tutorials closely and have the black phone taken apart as far as getting the logic board out. But this is a big different from a "screen replacement". Before I go further -- and there are a number of additional steps still -- I'm wondering: Can I just put the white phone's logic board into the black phone, then put the black phone back together? Or do all the parts from the white phone -- down to the screens -- have to go together into the black's covers?

The point of this would be to prevent taking the black phone all the way down to its front screen only, which involves a number of steps past where I am. Currently I have the logic board out of the black phone (and the preceeding parts of the procedure involved in getting to it), and ready to receive the white phone's logic board (if this would work), then go back together.

Would this work, to just swap logic boards?

Or do all the parts in the white phone have to go together into the black shells?

Hope this makes sense, I'm waiting tools in hand, thanks very much for any help.

Thank you!

Neil