Even his 820 is not granted by Xmas, he should still have his 457. You need to check when his 457 expires. When it does, the bridging visa A will come into effect. If his 457 won't be expired for while, then you don't have to worry about it. If it is going to expire around Xmas and BVA takes place, then you need to Bridging Visa B to allow him to travel and enter the country again.
Also, When it comes to early December, assumed that you have a CO and haven't been granted the visa yet, you should notify your CO that he is traveling so that CO will hold up the grant until he comes back or grant him the visa before travel if that was to happen around that time.