Users are unable to edit 'Notes' that are created by another user. You will see the 'Edit' button icon in Salesforce Classic. However, if you click on it, you will not have the option to type within the box nor will you have the option to 'Save.'
In order to allow a user to Edit Notes created by another user, the one who created the Note will have to share it by using the Note Sharing Settings.
Note: 'Edit' action is only available in Classic. "Notes" can only be shared for viewing access in Lightning.
1. Click the tab of the Object where you created the Notes.
2. Click the name of the record where you created the Notes.
3. Scroll down to the Notes related list.
4. Click the title of the Notes you want to share or be edited by another user.
5. On the right side of the page, under the 'Shared With' section, you will find 'Note Sharing Settings.'
6. You will see three dropdown choices: Share with people, Share with groups and Sharing Settings. Select either Share with people or Share with groups .
7. A box will appear where you can type the name of a user or group. Select the name.
8. Select whether the User or Group will have Viewer or Collaborator access.
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