If I understand correctly, address A belongs to Alice. Address A can send to any address upon the signature of address A.

Address B, belonging to Bob, Alice’s son, (the associated private key) can also cause unspent outputs from address A to be sent from address A to address B. The private key associated with address B can spend any output from address A, but only after x blocks since a transaction was sent to address A from address B. Address A can spend any output from address A to address B at any time.

The above means that the benefactor can spend some of his coin without having to provide an updated transaction or key to the heir.