FirmwareManagement.UpdateFirmwareRequest operation should update DeviceFirmwareHistory (device_firmware_file table in osgp_core DB) after successful installation of new FW.
There is a separate FirmwareManagement.SaveCurrentDeviceFirmware operation that can be used to manually update DeviceFirmwareHistory, but I assume that this operation should be used only if FW is not installed via GXF.
Please let me know if you need any other info or assistance.