That is going to be an issue. The pin-out is likely proprietary to an expected HP config that is NOT likely to work with a standard (non-HP) motherboard.
It can be made to work by making your own fabricated connectors and plugging them into that connector. However, you would still need to determine the pin order.
Well, photos of connectors that "do stuff". I haven't gotten into it in awhile, to be honest I usually maintain 2 laptops. I found it oddly difficult to find a proper service manual for this HP model, like that would have good pictures of what connects to what. So I will stand by my original advice of seeking YouTube's help.
The motherboard that was previously in this was the AAHD2-HY rev 1.03. The connectors seemed to be labeled the same on the motherboard. I plan on using the ga-78lmt-s2
Actually I tried a different search approach, and did get led back to HP's site, where I tried expanding more [+] sections. I found a rudimentary motherboard schematic. It's in the [+] section "Motherboard Layout". Hope it helps, can't imagine I can do anything more. https://support.hp.com/us-en/document/c02966470