Configure computer B to add a transaction from the address in computer A, but not broadcast to the network
Once computer B mines a block, withhold the block and broadcast transaction
Release the block and put Computer B back to normal solo mining
The coins are now in a block subsidy
You don't actually have to broadcast the transaction at all - the block is still valid even if the transaction was never broadcast. In fact you don't want to broadcast it because that significantly increases the risk of something going wrong and you losing your bitcoins. Doesn't stop malicious attacks though.
Also: this scheme will stand out like a sore thumb to everyone watching Block Explorer and probably get mentioned on IRC.
Some variation of this 'scheme' is inevitable. When Wal-Mart is mining, they might reject fee paying transactions from known Target addresses; and withhold some of their own transactions to be included only in self generated blocks. If Wal-Mart (or other large, international corporation) were to consolidate all of the small transactions they produce in a given day (that can be delayed) into a single, self-generated block, they might stand to save a fortune in fees. This assumes that Wal-Mart has enough miners to reliablely generate at least one block each day (or week, month, whatever). Once this is commonplace, it will become very difficult indeed to discern this kind of delayed transaction processing for economic reasons from delayed transaction processing for anonimity reasons.