Well, I did touch on two topics, first, to get it out of the way, the filter cartridge or media you are using or will be using when you get your betta in this tank will be useful if you decide you want another. Or need another.
Since you will have had a filter running for your first tank it will have become seeded with beneficial bacteria that you can use to set up another tank . Really not related to your question, though.
Now to address your concern...
Specifically...This Fluval product is a pre-filter for one of their models (the Edge). I use it on the out-flow portion of the filter that flows out into the tank . So, this would be the "duck bill" part you are describing .It fits over that part like a sleeve. They are usually a good fit, but I didn't get a clear look at your filter. Can you post a close-up or tell the model?
(And yes, there are sponge filters with airline tube and electric air pump but that's a different thing, and way too bubbly for betta).
I hope this makes sense...
If you are still unclear I will post an image for you tomorrow ☆
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Yes, it’s clearer now
Pretty busy with work this week but I’ll post current filter setup when I have a chance.