No patience here, just sharing experiments 
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I’ve test inbox notification on the first shot of Solidarity Chat Solidarity (just swipe to the right to see your inbox messages) there is a ChatTest channel where you can do some tests. The arrow button allows you to reply & send notification if there recipient has well configured his inbox
Here is how each inbox folder must be configured Solidarity - first shot for a 🐈 - #5 by Smag0
Here is how Solidarity post a notification to the inbox friend solidarity/input-simple-element.js at eaf8ff8e10829e40de336b3ce8a32dccb8e9c20a · scenaristeur/solidarity · GitHub
Feel free to ask if this is not clear
@jeffz solid-file-client is one lib that say "be sure your app is authorized " but there is no problem with the app it’s a problem with the webid’s rights. I’ve discovered that recently but not have the time to post an issue yet . It’s a little bit confusing as it (I think) create first the file then patch it. That was the propos of my previous post. So first try to enlarge authorization when you dev , to not be blocked.
If it’s 401, that means that only the authorized user can post. If it’s 403, that means that the app is not a trustedApp , but I encountered some other when dev my last app with create file function : my app is correctly authorized, when ‘everyone’ is granted to Poster level I have a’ 403 verify your app auth’ and when I upgrade the ‘Everyone’ to Editor level the file is written.