Notes

Just to confirm you want to add someone to collaborate with on a note

This is an awesome feature that Apple offers.

Please confirm first of all that you are in the iCloud sector of notes app

This is a good resource on sharing notes : https://support.apple.com/en-us/HT206987

Once you open the note, you tap on the more button (...) then tap share note, then you may tap on sharing options and enable or disallow permissions for the note.

Hope this helps ;)

Make sure that the person that is trying to edit it has notes turned on in iCloud settings

Settings > name > iCloud > notes