Extracting firmware from a device for reflashing?
If it isn't the overlapping WiFi channels: a normal Nandroid does include /system and /data, but I think you can just flash them separately. What you're referring as "firmware" is probably the /system partition. 

If you guys are using the TWRP recovery, you should be able to add his entire TWRP-created recovery onto your device, boot into TWRP and start a restore, but simply uncheck all partitions except /system. I would make a Nandroid backup before attempting this, as it should work, but I'm not certain.

If you guys aren't using TWRP, it's possible manually via a straight adb dd copy (but...it's not perfect): http://www.modaco.com/topic/327661-how-to-backup-the-systemimg-bootimg-and-recoveryimg/

Basically, as that thread states, on his device, use adb dd to copy a system.img from his phone onto his /sdcard. Then, on your device, use adb dd to paste that system.img onto your phone. Things that need answering: what partition block is /system on (mtdxx) and whether the pull will actually create a full system.img (they note that this method doesn't always copy all of the /system partition).