The other person does not need to be online nor does he/she need to know about the transaction. The bitcoins are sent to the network. The next time this person opens her client the bitcoins will show up there.
Who make the transaction must be online, to send it to other nodes so that eventually it will be put in a block in the blockchain.
The partner is not required to be online, transactions are registered in the blockchain, that is the same for everyone
Thanks for the answers, bitcoins are so cool
I have so many more questions, a bit more technical in nature but they'll have to wait!