IOS – Transferring notes into a particular folder

Syncing the notes to your computer, then moving the notes to your email notes and letting it sync back to the phone would be the easiest.

Without syncing you could email each note to yourself by clicking the envelope icon at the bottom of each note. Then turn it into a note in your email account, of course this would take a long time but you wouldn't have to sync with your computer.

Using OSX 10.8 it is simply not possible at the moment, what you need to do is to access a Mac running 10.7 or lower and sync them to that Mac and move them to an IMAP notes account. Then, you can access the IMAP notes in 10.8 Notes app and drag them all to iCloud. The only manual part necessary is to remove the duplicate notes left "On your iPhone" - they need to be removed one by one (or simply left alone).

Details:

1. Turn off iCloud Notes sync (Settings -> iCloud -> Notes switch to Off)
2. Set up an IMAP account in Mail on both computers (running 10.7 and 10.8)
3. Set up iTunes synchronization with the Mac running 10.7 (Make sure to select to synchronize Notes in iTunes)
4. Synchronize with iTunes
5. Go to Mail in 10.7 and drag the notes "On your Mac" to the IMAP notes folder
6. Turn on iCloud Notes sync (Settings -> iCloud -> Notes switch to On)
7. Open the Notes app in 10.8 and drag the notes from your IMAP notes account to the iCloud notes account
8. (Optional) Switch to your "On my iPhone" notes account and remove all notes, one-by-one, in order to avoid confusion later.
9. On your phone, make sure that you are using the iCloud notes account (Notes -> Accounts -> iCloud) when using notes