The F4A51 has an internal screen pickup. It is not servicable unless the transmission is disassebled. Older versions of this transmission had a "spin on" type filter mounted on the top, but this filter was discontinued on later models.
To replace the transmission solenoids on an F4A51, first, ensure the vehicle is on a level surface and disconnect the battery. Remove the transmission pan and filter to access the solenoids, which are typically located on the valve body. Carefully disconnect the wiring harness and remove the retaining bolts to take out the old solenoids. Install the new solenoids, reassemble the transmission pan and filter, and refill the transmission fluid before reconnecting the battery and conducting a test drive.
The 1999 Hyundai Sonata GLS came equipped with the 2.4L 4-cylinder and 2.5L 6-cylinder engines. Both engines had the F4A51 automatic transmissions. As of September 2014 the newest and downwardly compatible automatic transmission fluid specification for the application is Hyundai SP-IV.