These battery boards can likely be swapped. But I would not recommend it and it will require soldering or spot welding to transfer it over since there are no easy connectors to sever or remake the connection to the battery.
It looks like you purchased this battery from iFixit if I am interpereting the pictures correctly (iFixit logo visible in pic 2). If so, I would get in touch with [link|https://help.ifixit.com/?pk_vid=8469243d14b61623167007499223ff49|customer support|new_window=true] and they'll get you squared away.