Other sources suggest that the Tera Grand-branded adapter shown on the product page they sent you has an FTDI chip inside, same as the cable you're using. Really, the only thing that could differentiate the two is the cable - there's a possibility that the scale actually doesn't want a null modem cable, so if you have one of these kicking around, or you can wait a couple days for Amazon to send you one, I'd try it before paying A&D's ~200% markup on the part they want you to buy.
This is the exact adapter I have, made by Tera Grand, and it came with a 3-foot USB extension cable and a mini CD with drivers for Windows 98, 2000, XP, Vista, Windows 7, Mac OS 9, and Mac OS X:
https://www.amazon.com/dp/B00BUZ0K68/?th=1
Adapters with built-in cables are also available from Tera Grand, with lengths of 3, 6, and 10 feet. With these, your choices of mounting hardware are either thumbscrews or hex sockets like you'd find on the back of a desktop PC; with the one like mine, all you get are thumbscrews. I took the thumbscrews out of mine because they were getting in the way.
Either way, I hope this helps. :)
>https://www.amazon.com/dp/B00BUZ0K68/?th=1
Thank you mate. :) Wasn't quite sure which adaptor to buy on Amazon. Thanks again.