Hi -- not quite sure what you are after?
DVI and HDMI digital video signals are essentially the same. So an adapter from DVI video to HDMI video is just a passive plug adapter. These can be had on ebay for a few $.
On the other hand, DVI does not carry an audio signal. (At least regular DVI does not; I believe there are some non-standard extensions which "abuse" some pins on the DVI connector to transmit audio.) If you have analog audio outputs only, and want to mix these into the DVI signal stream to obtain a complete HDMI signal including audio, that's definitely not feasible with a passive adapter only. The little PCB you have photographed does not look like it's capable of doing that either. (Although you mention that it receives audio signals on the large connector?!)
Could you please explain what output signals you have on your Amiga, and what you need to generate from them?
Edit: Typos