Mod HRAP2 SA with Seimitsu LS-32

I want to mod my HRAP2 SA with a LS-32 stick. From what I can find by searching through old post, I think I will need a S mounting plate for it. So here is the stick that I find at akishop: https://www.akishop.jp/joysticks/164-ls-32-ss-lb39.html

Does anybody know if this stick is going to work with HRAP2 SA? Do they use the same connector? Is there anything else that I should pay attention to?

I should mention that I feel HRAP2 SA stick's engage range is a little too long. So I wonder if this LS-40-SS would be easy to install too: https://www.akishop.jp/joysticks/168-ls-40-ss.html##

Thanks!