Can fighters transfer from one barrack to the other?

Yes you can move troops to any position in any APC (barracks). Tap on a barracks building to manage the troops in that APC formation. Or tap the truck icon on the upper left of the screen to view all the APC's at once.

Tap the cog icon in the top right of each APC to manage the heroes and troops in them. In this screen you can drag and drop any set of troops from below to each of the positions and also assign heroes to any unlocked hero slots from the hero tab.