Make updates to shared folders in Notes on iCloud.com

You can share folders and make updates to their contents. All participants of the shared folder see any changes made to the folder.

Go to icloud.com/notes, then sign in to your Apple Account (if necessary).
Select the folder you want to update in the sidebar.
If you’ve been invited to edit a folder but haven’t accepted the invitation, you need to click the link you received, then click Open in Notes. After you open the folder for the first time, it appears in the sidebar on iCloud.com and on your iPhone, iPad, or Mac where you’re signed in to the same Apple Account.
Edit the notes within the folder.
When someone makes an update to a shared folder or to the notes within a shared folder, everyone sharing the folder sees the changes, but no one can see who made them. If an edit is made to a note in a shared folder, the timestamp below the note in the notes list shows the last time it was edited. If you’re not currently editing a shared note, a yellow dot appears next to the note in the notes list when someone else edits it.

If you were invited to edit a folder using an email address or phone number that isn’t associated with the Apple Account you use for iCloud, ask the owner to resend the invitation using the correct email address or phone number. You can also follow the onscreen instructions to associate that email address or phone number with your Apple Account.

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iCloud User Guide

Make updates to shared folders in Notes on iCloud.com