You can't currently transfer purchases/downloads from one account to another account.
When you download past purchases from an account then you will potentially tie the device (or computer if you do it on that) to that account for 90 days : http://support.apple.com/kb/HT4627
Have you got the ibooks already on your computer and/or on a backup so that you can sync them to your new iPhone ? If not then have you bought anything on your new account yet - could you go back to just using the old account ?
If they are PDF downloads then I assume that they weren't from Apple (?) - in which case they shouldn't be tied to an account. Do you have them and/or what was purchased via that account on a backup ? If you do then you should be able to authorise that account on your computer's iTunes (via the Store > Authorise This Computer menu option) and add them to your library via File > Add To Library, and then sync them to your phone.