Swapping Logic boards form a 32 GIG to a 16 GIG

So recently I bought a Bad ESN verizon iphone 4 which was 32 gig in farely new shape

I currently have iPhone 4 Verizon which is 16 gig

Couple weeks ago i cracked my screen and was searching for a low priced LCD because ill soon be upgrading but instead I bough this phone for which i thought was a pretty fair deal

Is it possible to put my CLEAN esn 16 gig logic board in to the the the Bad esn 32 gig iphone 4 cdma

I mean ill basically be swapping them out but will it accept a lower memory ? please let me no THANKs