Well in order to find out why the "solution" is not working you will need to break it down and test the parts. Assuming all is ok with your MMI system, my experience of this setup is that either the HDMI Box is not working as many of these are very cheaply made, the RCA to AMI cable is not the correct one needed or it's a cheap reproduction thats faulty.
If you cannot connect the complete solution to a TV or monitor then I would look to test the RCA to AMI cable by connecting a device like a digital camera to it via the TV out cable many are supplied with. The lightning to HDMI and HDMI cable you can test by connecting to your TV. Start a process of elimination.