Can only reiterate. Data such as a directory can be stored either on the SIM card memory or in the handset memory. Usually where the directory is stored is settable on the phone settings. It sounds as if your directory is on the handset.
If you still have it is is a faff but you can first copy whatever is presently on the SIM to the new handset. Always check it's copied before selecting but next delete all on the SIM, put it in the old handset, copy the handset data to the SIM, put the SIM back into the new phone, copy the data from the SIM to the new handset.
If you have a lot of data you may need to transfer it over a bit at a time.
Alternatively if your handsets are both capable of connecting to a PC and transferring data as backup/restore there are applications that will allow you to do this via your computer.