The FAA will validate your EASA PPL. This is not an actual FAA certification. It is based on foreign pilot privileges/restrictions and medical. For instance, pilots from Mexico cannot fly VFR at night. European pilots need a night endorsement. If you have a private, commercial or ATP, the FAA will only give you private pilot single engine privileges as a courtesy to fly “N” registerd aircraft.

You will need to contact the local FSDO or the FAA in Oklahoma to see where your civil air authority needs to send your records. I suggest you do this far in advance. You will need a FAA flight instructor to give you a flight review and endorse your logbook. The inspector at the FSDO will speak to you and “test” your English comprehension.

If you meet all the flight experience requirements for the FAA private pilot certificate, you can obtain an actual FAA certificate. You will need to take the written test and pass a checkride with an examiner. You will also need to obtain an FAA medical.