The flame transfer function (FTF) of an industrial lean-burn fuel injector has been computed using large eddy simulation (LES) and compared to experimental measurements using the multi-microphone technique and OH* measurements. The flame transfer function relates the fluctuations of heat release in the combustion chamber to fluctuations of airflow through the fuel injector and is a critical part of thermoacoustic analysis of combustion systems. The multi-microphone method derives the FTF by forcing the flame acoustically, alternating from the upstream and downstream side. Simulations emulating this methodology have been completed using compressible large eddy simulations (LES). These simulations are also used to derive an FTF by measuring the fluctuations of mass flow rate and heat release rate directly which reduces the number of simulations per frequency to one, significantly reducing the simulation cost. Simulations acoustically forced from downstream are shown to result in a lower value of the FTF gain than simulations forced from upstream with a small change in phase, this is shown to be consistent with theory. Through using a slightly different definition of the FTF, this is also shown to be consistent with measurements of the heat release rate using OH* chemiluminescence however these results are inconsistent with the multi-microphone method result. The discrepancy comes from not having an accurate measurement of the acoustic impedance at the exit plane of the injector and from certain convective phenomena that alter the downstream velocity and pressure field with respect to the purely acoustic signal. All simulations show a lower gain in the FTF than the experiments but with good reproduction of phase. Previous work suggests this error is likely due to fluctuations of the fuel spray atomisation process due to the acoustic forcing which is not modelled in this study.