Many club players stick to their "point coint" and would all open 2NT, balanced 20-22 with the South hand and, as per the example, jump to 4 after their partner transfers via 3.  This takes away loads of bidding space and partner never knows when to go on or if they are always maximum with 3 or even 4 card support.

Today's South hand is far better than the 22 points it has.  I would recommend opening it 2.  Maximum with all Aces and Kings, a good 5 card suit with two 10s make it worth upgradng to a Game Forcing opening bid.

Perhaps the bidding should go say : 2 - 2 - 2NT - 3 - 3NT - 4 - 5 - 6

A little explanation... 2 is Game Forcing and after a negative 2 response denying and Ace and a King, South now tells a little white lie and shows 23-24 points balanced.  North transfers and South "BREAKS" the transfer with 3NT.

One to agree with your partner is to bid 3NT with a maximum, three card support and no Jacks in the 22 points.  With maximum, FOUR card support and no Jacks, you would bid 4.   With any other holding including a maximum with four card support and Jacks in your hand you should ALWAYS accept the transfer and see what North does next (he may Cue bid - you know he has no Aces).

The 4 bid is a "re-transfer" to Spades to get South to play the hand.  The jump to 5 asks if North's trumps are "very good".  North should pass with poor trumps and bid 6 with very strong ones.  The slam is bid and makes easily for another "top" on the way to your 60%+ score with only29 HCP.

It's an easy game.