Global Itach Flex wifi adaptor same as Roomie's version?

I have 2 of the branded older branded Roomie (or Simple control) Itach flex wifi adaptors and just wanted to make sure I could use the Global Cache FLC-SL-232 Flex Link RS232 cable with it.

I need rs232 control, which has more control options for an Epson LS12000 projector vs the standard infrared codeset.

https://www.amazon.com/Global-Cache-Serial-RS232-FL-SL/dp/B01ANXDEEM/ref=sr_1_1?crid=1Z4HET1CT9MZ4&keywords=Global+Cache+Flex+Link+Serial+Cable&qid=1671723890&sprefix=global+cache+flex+link+serial+cable%2Caps%2C171&sr=8-1

The correct cables should be linked in several places on the website.

Here is the normal RS-232 cable:

https://amzn.to/3HWMCJK

Here is the other one, a mini RS-232 cable usually used for Samsung TVs and a few others:

https://www.walmart.com/ip/Global-Cache-GCFLCSLMJ-6-5-ft-Flex-Link-RS232-Mini-Jack-Cable/865496712

(I can't find the right Amazon link at the moment for the mini jack cable, clearly there is some problem there, I've ping'ed Global Caché.)

Thanks Will. I just ordered one (below), which I believe is the one you referenced.

https://www.amazon.com/gp/product/B01ANXDEEM/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

looks like I grabbed the last one in stock on Amazon. Thanks again