Unfortunately the TL866II Plus programmer can read but cannot write to the FM24C04B FRAM. For more details see this thread on the EEVBLOG forum. An HP 34970A I bought some time ago had the classic 74x calibration errors caused by the FRAMs.
So I though the fastest way to program the FRAMs would be to write some arduino code for my I2C Memory Programmer. The program needs a table called pages which hold all the data from the FRAM. It can then program the FRAM with the contents of the table or verify them against it. If you need to create a pages table you can read the contents and copy the output to the code. You will have to reload the program to the arduino.