OP, as has now been said many, many, many times, it is honestly this simple:
Patreon will send $720 to your bank account.
You now send $360 to the other person's bank account.
Honest to God -
That is all there is to it!
The other person does not even have to send you an invoice. the IRS, DOJ, your Mom, nobody cares about invoices.
You just do that each month.
How you do your taxes
When you use taxact.com or the others to do your taxes, you tick "self-employed".
When you do that, there's a slot where you type in "gross income", you'd enter $720. There's a slot where you type in "expenses", you'd enter $410. (So, you paid $50 for office supplies, and the $360 above = $410.)†
That's all there is to it.
There are no further details.
There's nothing else to do, think about, know, or consider.
This happens constantly and millions of times a year with 16 million people.†† It's a total non-issue.
There is no "partnership", "LLC", "St Nevis Holding Corp", "Accounting", "Accountant", "Agreement", "Contract" or anything else, whatsoever, involved.
It is, honestly, That Simple.
I (for example) have done this dozens of times. Noite that there are some 4? million apps on the appstore, at least 300,000 of them make more than a couple thousand bucks a year, and of those 300,000, 99.999% are handled as I say above. It's a total non-issue.
How does Colleague do their taxes?
The $360 is "gross income" - that's it.
Could someone be ripped off in this?
Sure - you could FAIL to send the $260 to Colleague. But exactly the same thing applies if, incredibly, you had some sort of joint bank account!!!!!!!!!
It happens EVERY DAY that a pair of people doing a business, who have a joint bank account, and, one or the other rips-off the other. There is no solution to that!
What you do is simply, every month one sends the other the half-dollars.
If, one month, that person rips off the other - that's the end of it. What else can you do?
There is no corporate or other structure that can avoid such problems.
You have heard of Facebook of course. (It's like tiktok for incredibly old people!) Facebook is this one group of guys who stole a business idea and formative technology from this other group of guys. All the lawyers and business formulations in the world were involved, but "rip off" still happened. (The original guys got a few dollars in the end, years later.)
† taxact actually has different slots in the web form like "office supplies" "repairs to iphones" etc. in the example, the overall amount is "410".
†† about 16 million self-employed in the US as of writing.